A System Dynamics A pproach to Modelling Business
Activities of Ukrainian General Insurers
Pervin Dadashova
PhD Student, National University of “Kyiv-Mohyla Academy”
Kyiv, Ukraine
dadashova.pervin@ gmail.com
Anton Lytvyn
PhD student, National University of “Kyiv-Mohyla Academy”
Kyiv, Ukraine
anton.v.lytvyn@ gmail.com
Abstract
In this paper, a system dynamics model of a Ukrainian general insurer is presented. The aim
of the study is to examine the potential feedback effects related to the dynamics of profitability of an
insurance company. The developed model follows the managerial accounting logic, which combines a
traditional accounting approach with non-financial elements. The model structure consists of twelve
interconnected modules, each representing a relatively detached sphere of insurer operations. The
major feedback loops that determine the dynamic behavior of the model are based on a combination of
different business activities. These loops produce both reinforcing and counteracting effects that
influence the financial performance of an insurance company and are centered around insurance rate,
insurance premiums ceding, and investing. The test of model responses to different demand shocks
allowed to corroborate the prominent feedback impacts and outline possible implications for
managerial practice.
Keywords: general insurance, business modelling, managerial accounting, cash flows, balance
sheet, underwriting, reinsurance, reserving, investing, financial results, Ukraine.
Introduction
The objectivity and reasonableness of business decisions in general
insurance companies have always been in the spotlight of both corporate
managers and governmental officials. The former are mainly interested in
high business performance, whereas the latter are concemed about
solvency of companies. In times of crises, the soundness of corporate
administration activities becomes even more urgent since it largely
determines the ability of a firm to endure adverse operational conditions
and continue as a going concer.
It appears that the effectiveness of management in Ukrainian
general insurers has been rather low. Indeed, the National Commission
for Regulation of Financial Services Market of Ukraine (NCRFSM)
reports that the crisis of 2008-2009 has shown that many insurance
companies (as well as other companies in the financial sector) were
unable to cope with unexpected difficulties, high rates of bankruptcy
being a logical consequence. According to NCRFSM data, during 2005-
2008, the number of registered general underwriters rose from 348 to
396, and by the end of September 2014 their number decreased further to
331. The mean drop-out rate for the last 5 years has been above 6%.
The main reasons for the rising number of bankruptcies of
insurance companies are low profitability and depletion of cash stocks.
The NCRFSM’s online register shows that most Ukrainian general
insurers had their licenses suspended and nullified due to the large and
recurring proportion of non-settled claims. Insufficient cash levels cause
insurers to become insolvent, which is the primary indicator for the state
regulator to initiate bankruptcy proceedings. For instance, one of the
functioning Ukrainian general insurers, PJSC “Etalon” insurance
company” has faced problems with settling insurance claims in 2014 and,
as a consequence, temporary administration in the company was enforced
by the state regulator (NCRFSM). However, viewing insolvency as a sole
cause of insurance company means neglecting the real roots of this
problem that lie in the structure of insurer business processes. For
example, the problem might be connected with poorly managed financial
flows due to flawed corporate policies.
Limited scientific and practical attention to the specifics of
Ukrainian general insurers business hinders the comprehension of key
causal relationships that influence the problematic behavior of the
companies. Many domestic scientific works have been aimed at
theoretical discussion on financial health of insurers, yet many them
either suggest utilizing outdated or irrelevant methods, or simply rely on
overviewing such methods (Dobosh, 2009; Kryvytska, 2012). Fewer
works have been dedicated to predicting financial crises in insurance
companies, however, they do not present clear guidelines on how to cope
with identified undesirable conditions (Lee and Urrutia, 2006; Kleffner,
et al., 2009; Shpitzhluz, 2013; Zhuravlova, 2013). Finally, even fewer
authors in Ukraine have addressed the need of establishing holistic
frameworks for managing complex business systems of insurers (Barlas
et al., 2000; Klepikova, 2011).
General insurance business has several peculiar features stemming
from the nature of its main operations. Firstly, insurers are corporations
that provide financial services and, therefore, do not have a common
inventory (Hamankova, 2007; Zweifel and Eisen, 2011). Secondly, the
amount of contractual obligations of general insurance companies is
probabilistic, thus they have to deal with more significant risks
comparing to companies in other industries (Zweifel and Eisen, 2011).
Finally, the activities of insurance corporations are subject to strict state
supervision and regulation due to the uniqueness and importance of
services they provide (Hamankova, 2007; NCRFSM).
Both the distinctive characteristics of insurance business and the
gaps in scientific knowledge in general insurance sphere make the
research on insurance company business processes quite topical. System
dynamics should be a promising instrument to be applied in the research
on the problem due to several reasons. Firstly, the dynamics of the
financial performance of insurance companies appears to be complex and
non-linear, extending beyond simple “gather premiums — pay claims”
algorithm and depending on numerous internal financial restrictions
(Hamankova, 2007) that might imply feedback effects. Secondly, the
factor of time has quite a significate influence on cash flows of insurers:
premiums take time to be fully earned, investment instruments have to
mature before they can yield income, etc. (Hamakova, 2007; Zweifel and
Eisen, 2011). Finally, the management policies in general insurers can be
associated with mental models the influence of which has to be examined
to determine their real effect on the financial condition of the companies.
The aim of this work is to develop a model of a Ukrainian general
insurance company based on the available insurance corporation theory,
accessible firm data, and relevant legislative regulations in order to
determine the key feedback relationships responsible for the dynamics of
profits or losses and their effect on cash accumulation in general insurer
activities. The built model should both facilitate the traditional analysis
of financial condition of insurance companies and promote better
management decision making.
Overview of the Model
The developed model reflects most major activities of Ukrainian
general insurers. Just as the other enterprises, general insurance
companies perform three main types of activities, namely operating,
investing, and financing ones, and it is the content of these activities that
distinguishes insurers from other types of businesses (Hamankova, 2007;
Klepikova, 2011).
The operating activities of an insurer consist of underwriting,
reinsurance, reserving, and claim settlement. Underwriting includes
signing insurance contracts with a specified insurance sum based on the
capital available. If the company cannot retain the proposed risk,
reinsurance is used. Part of gathered premiums are reserved to ensure the
ability to settle claims in form of payouts.
However, unlike firms from other industries, insurance companies
have a stronger imperative to accumulate and multiply funds gathered
through insurance operations. Investing serves a major role in business
activities of a general insurer since it can provide the required addition of
funds. Insurance companies can invest both free funds and technical
reserves, but the latter are subject to strict regulations by the government.
Financing activities represent insurers’ flows related to attracting
and returning financial resources to/from both equity and liabilities, as
well as show payouts to owners in form of dividends.
Despite the fact that typical statement of cash flows presents
financial flows within the mentioned three activities, we suggest
departing from a solely accounting approach during the modelling
process. Forrester states that financial information “does not form an
integral part of decision-making functions” and “the skeleton framework
of primary effects within the organization can often be represented
without financial and accounting information’”(1961, p. 335-336), yet the
financial dimension is extremely important for proper management in
insurance companies. To take into consideration both financial and
nonfinancial aspects of insurance business, the managerial accounting
perspective was chosen for modelling.
Management (or managerial) accounting is “the part of accounting
devoted to providing information useful to the management of an
organization, (...) contrasted with the process of producing official
accounts”; it “involves the collection and processing of information
which will help in actually running a firm” and “includes checking on
stocks to ensure that enough are kept to avoid running out.” (Black et al.,
2012, p. 193).
Managerial accounting information appears to be most suitable for
purposes of business modelling due to several reasons. Firstly, unlike
pure accounting data, management accounting information provides a
broader view on the activities of the company and, thus, enables the
analysis of core causes in dynamic business behavior. Secondly, this kind
of information implicitly or explicitly accounts for managerial mental
models that are built in the business model of an enterprise. Finally,
obtaining such information is feasible (in contrast to perfect market
information, which virtually cannot be gathered and utilized in decision-
making).
Financial reporting tia Financial flows
information
Financial
stocks
Physical ——
vedo Physical flows
Financial
stocks
Financial flows
‘Accounting information
Financial flows
Managerial accounting
infromation
piers } Physical =p)
Enterprise boundary
Other stocks Other flows
Figure 1. Corporate financial statements information structure from
different reporting perspectives
Moreover, the managerial accounting perspective largely coincides
with the system dynamics viewpoint on the problem (See Fig. 1).
Financial reporting data mostly presents financial statements disregarding
any stock-flow relations between them. Accounting information, which is
more detailed, includes a broader view on financial statement formation:
the dynamics of flows influencing stocks can be examined. Yet, the
accounting approach limits its scope only to direct causal relationships.
By contrast, management accounting perspective does not suffer scope
problems and can provide enough reasoning not only on causal, but also
on the feedback effects in corporate activities.
The developed general insurance company model currently
consists of twelve modules, each representing a relatively detached
sphere of corporate activities. Most modules are interconnected, showing
that either information or financial flows are shared between them. The
modules included in the model are the following:
Actuarial (insurance rate calculation),
Underwriting (insurance product sales),
Reinsurance (calculation of allowed retention and reinsurance
related financial flows),
Claims (keeping track of contracts, contractual liabilities
settlement),
Reserving (formation, investing, and returning of insurance
reserves),
Human resources (track of sales and administrative staff and
their productivity),
Investing (investing and returning of free funds),
Fixed assets (track of fixed assets),
Equity (formation of retained earnings / accumulated losses,
track of statutory capital and equity),
Tax calculation (calculation of tax),
Financials (calculation of aggregate asset, equity, reserve, and
liability statements, evaluation of financial ratios),
Cash (track of cash, incorporation of all cash flows).
Figure 2 shows the outlay of the modules. The color scheme was
applied in order to simplify spotting of feedback loops between the
spheres of insurer activities (inputs within each module are presented in
corresponding colors).
Actuarial
Fixed \
assets
h\
Financials
Figure 2. The proposed activity structure of a general insurer
Our approach to accounting operation presentation is largely based
on the works of Yamaguchi (2003) and Melse (2006). The insurer
activity framework follows the legislative base on insurance market
regulation (NCRFSM) and studies on insurance economics (Hamankova,
2007; Zweifel and Eisen, 2011).
A general insurer attempts to satisfy the demand for insurance
products by supplying its services at a price of gross insurance rate
(Actuarial) based on the available sales workforce (Human Resources)
and fixed capital (Fixed assets). The gross insurance rate is formed with
taking into account the anticipated costs associated with underwriting and
claim settlement, the risk premium, and the historical insurance loss rate.
Insurance rate formation premium process is presented in Fig. 2.
The sales of an insurer are its gross premiums written
(Underwriting). Every general insurance company has to maintain an
unearned premium reserve, which is calculated based on premiums
written for three previous quarters (Reserving).
Yet not all written premiums belong to the company. Based on the
allowed retention, certain amount of gross premiums has to be ceded,
which influences the actual amount of sales pertaining to the insurer
(Reinsurance). The reinsured part of premiums is also taken into account
in the unearned premium reserve as a claim right to a reinsurer
(Reserving). The exclusion of premiums ceded combined with the period
change in the unearned premium reserve results into net premiums
earned, which are the actual amount of an insurer’s revenue that is taxed
at a 3% rate (Underwriting).
A general insurer keeps track of active, settled, pending, and
expired contracts. When claims are presented to an insurance company,
their validity is checked and the amount is compared to the insurance
sum; after this, an insurer proceeds to making payouts (Claims) if there is
enough cash (Cash). Reinsurers compensate part of claims based on the
share of ceded premiums in gross premium written (Reinsurance). The
amount of premiums that was previously reserved into the unearned
premium reserve is returned from reserves if the corresponding contract
has been settled or has expired (Reserving).
If there is free cash (not reserved and not used for other payments),
it is invested into different assets in order to produce additional non-
insurance revenues (Investing). Likewise, insurance reserves are invested
into different types of assets, however, reserve investing is highly
regulated legislatively (Reserving) regarding maximum shares of assets,
their liquidity, security, yields, and diversity. Tax to be paid (Tax
calculation) is calculated based on insurance revenues (Underwriting),
10
other kinds of income (Cash), and salaries (Human Resources). The total
tax is presented as a separate outflow due to the highest priority of this
payment.
The retained eamings / accumulated losses are calculated based on
all cash and non-cash flows and constitute a part of total equity of a
general insurer (Equity). Insurance and other liabilities (mainly backlogs
on each cash outflow), as well as assets are aggregated into financial
statements. Additionally, financial ratios that can be used in evaluation of
financial health of an insurer are calculated (Financials).
The central and summarizing module of the model is Cash which
contains the general cash stock as well as all inflows and outflows that
affect it; additionally, cash stock is an input to many modules. Due to the
space limitations, most flows to and out of cash stock had to be
aggregated where possible.
The main inflows to cash stock are Insurance and reinsurance
premium revenues, presented as a separate flow due to the specifics of
taxation (3% tax is imposed on premiums earned). Other revenues (as
well as non-operating losses) are counted in the Other revenues or losses
flow, which includes Insurance payouts compensated (by reinsurers),
Other reinsurance related revenues (ceding fee and gainsharing),
Investing result (from investing of both free funds and insurance
reserves), and Fixed asset sales. It should be noted that investing results
are taken net of investing losses. All income presented in this flow is
taxed at a different, 18 % rate.
Other major flows are Reserving and returning UPR, Reserving
and returning RBNS, Reserving and returning IBNR, and Reserving and
returning ER. These four flows correspond to maintaining the unearned
premium reserve (UPR), reported but not settled claims reserve (RBNS),
incurred but not reported claims reserve (IBNR), and equalization reserve
(ER). Insurance reserves are kept at desired levels, any excess funds
being returned to the cash stock. Like reserving, Investing and returning
is a biflow to cash that shows the movement of free funds from the
general stock into certain types of investment assets and vice versa.
11
The main operating expense of a general insurer is Insurance and
reinsurance payouts. Another operating outflow form cash stock are
Insurance premiums ceded which denotes the sum of gathered premiums
that was reinsured. Costs and expenses (salaries and other costs), Tax
payment (insurance premium tax, income tax, and social tax on salary
fund), and Fixed assets purchases are the other outflows.
It must be noted that cash collection cycle has been simplified by
omitting accounts receivable (we assume that cash is collected right
away). In this case, it is possible to account for financial results based on
actual, not hypothetical cash flows. On the other hand, we have included
accounts payable into the model because their amount can be significant
in calculation of financial arrears.
Stock-flow diagrams for selected modules, as well as respective
equations are presented in the A ppendix.
The developed model produced behavior which is really close to
actual. The comparison of reference mode and simulation results are
shown in Graph 1.
950000) eesceesse sees nes cera ase ree ccna mene nee erESeeNCoRS
200,000
150,000 -
100,000 -
Time
Retained earings — —Retained eamings historical
— —Total assets historical Total assets
Graph 1. Reference mode and model simulation result
12
Testing Main Feedback Effects
The model contains several important feedback loops that
determine its behavior. Most of these loops extend beyond a single
module and include elements of different kinds of general insurer
activities. Fig. 3 contains the diagram with the main reinforcing and
balancing loops.
+ Contract
signed
+ Investing and
Demand for the company’s returning Gross insuran
services remiums written
al +, Allowed
Cash retentio
/ +
/ t Equitf
Share of insurance
sum to be reinsured
B2
| Profit or loss”
Total investing }
\ results
Insurance payout
compensation
Insurance premiums
ceded
Figure 3. Major feedback loops in the model (CLD)
The R1 reinforcing feedback loop shows the mutual influence
between the price of insurance product (gross insurance rate) and the
demand. The rise in demand for the services of an insurer positively
affects the number of signed contracts, increasing gross insurance
13
premiums. Higher sales allow insurers to reduce the net insurance rate
because of the falling loss rate, which, in tum, drives more customers to
the insurer’s products.
At the same time, gross premiums written can also rise not because
of an increase in contract signing but from the additions in product price.
The balancing loop B1 represents this feedback effect.
To demonstrate the feedback effects in the model, we propose
several tests. In order to examine the influences of R1 and B1 loops, the
ratio between the company’s insurance rate and the average market
insurance rate was changed as follows:
1. Average market insurance rate rises by 25% in Q4;
2. Average market insurance rate rises by 25% in Q4, and falls
back to the initial level in Q8;
3. Average market insurance rate rises by 25% in Q4, drops by
25% in Q6, and then comes back to the initial level in Q8.
Simulation results are presented in Graph 2.
B00;000 seeseeesss seeecsen cecceeec ee see tect ee ee eee ee ee eee
250,000
E 200,000
i 150,000
100,000 ---------------------------------------- == == -- == 22 --- == 2-22 een
BO000 seeker eee renee eee renee eee peru eee eens
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37
Time
— — -Gross insurance premiums Equilibrium
—— G1vss insurance premiums 1
—— Gross insurance premiums 2
——— Gross insurance premiums 3
Graph 2. Response of gross insurance premiums written to changes
in insurance rate
14
As it can be seen from the graph, the adaptation of insurance rate
to the average market level or loss rate enables the insurer to use this as
an instrument of rising its revenues in both auspicious and adverse
market conditions.
The second major reinforcing loop is based on the effect of
investing onto the cash multiplication. The R2 loop shows that the more
cash an insurer has available for investment, the greater will be the
financial results of such investments. This, in tum, increases the amount
of free cash that can be once again used in investing process.
Altematively, the extra cash can be directed to other outflows according
to their priority.
Reserving activities also include similar loops that show the
multiplication effect of investments. The major difference between the
investment of free cash and investment of reserved cash lies in
restrictions on investment shares and the need of maintaining the
required level of total reserves. The reserve investing reinforcing loops
are presented in Fig. 4.
ee
4 Cast? i UFR cash
“\peexoected stoc
\, pice gros
Rae
ua
Tata) UPR
ther bonds auutions*,
investments *
"Total UPR,
& stack addltigns:
Total UPR
other investment addition
Figure 4. Reinforcing loops within unearned premium reserving
(UPR) activities
15
The loop R1 characterizes the reinforcing effect on profitability
ranking through multiplying cash. At the same time, feedback loops
R2(R),.., R5(R) characterize the multiplying effects of reserve
investment in different assets (deposits, bonds, shares, and other) on the
reserve investing returns and cash. Since the effects of these reinforcing
loops are straightforward, testing is not conducted.
Another important reinforcing feedback loop presents the effect of
reinsurance on a general insurance company performance. The R3 loop
denotes that an increased premium ceding may lead to weaker
operational results, which negatively affects the equity of a company. At
the same time, equity is inversely related with the allowed retention,
meaning that premium ceding will increase the need to cede even further.
Apart from this, a major balancing loop B2 is connected with
reinsurance activities. Ceding premiums enables insurers to reduce the
required cash outflows related to insurance payouts, which positively
influences the operational financial result resulting into lesser need for
ceding insurance premiums. In order to test the effects of these loops, we
suggest changing the obligatory ceding norm from 0% to 20%. The
results are shown in Graph 3.
16
250,000 ----------------------------------- ==
200,000 -
2 150,000
§ 100,000. ee
50,000 -----------------------------
£
0 a
12 3 4 5 6 7 8 9 10 11 12 13 14 15
Time
—— Net insurance premiums eamed Equilibrium
Net insurance premiums earned
—— Insurance premiums ceded
—— Insurance payouts compensated
—— Period change in fraction of reinsurer in UPR
Graph 3. Effects of change in ceding norm on insurance premiums
earned and insurance payouts compensated by the reinsurer
The graph shows the introduction of mandatory reinsurance
practice lowers the actual insurance revenues of the company. At the
same time, the level of its claim expenses is lowered too.
The effects of all the abovementioned loops can be utilized in
management practice to find more effective decisions as a response to
market shocks. The reinforcing effects are useful in growth strategies,
whereas balancing ones may help to reduce expenses. We propose testing
several different managerial responses to the following shock in market
demand: rise in demand by 50% for a year with consequent decrease by
50% from the initial value for a year, and retuming to the initial demand.
Such management responses were tested:
1. The company does not respond at all;
2. The company adjust the insurance rate;
3. The company adjusts the insurance rate and invests;
4. The company adjusts the insurance rate, invests, and intensifies
reinsurance.
The results of simulation are shown in Graph 4.
17
1,800,000 ;
1,600,000
1,400,000 -
1,200,000
2 1,000,000
5 800,000
600,000 +
400,000
200,000 -
0
1 3.5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
Time
—— Equity Equilibrium —— Equity 1 Equity 2 Equity 3 —— Equity 4
Graph 4. The effect of different management steps on equity in
response to demand fluctuation
As it can been seen, the adjustment of insurance rate has a
smoothing effect on retained eamings, and thus on equity. It allows
managers to reduce losses when demand drops, but it also slows the
income growth. Adding investing to the policy enables reinforcing equity
growth. The effect of reinsurance is mixed: on the one hand, it limits the
losses, yet at the same time reducing the possibilities of growth.
Conclusions. The developed system dynamics model describes the
major spheres of Ukrainian general insurer activities from the managerial
accounting perspective. The structure of the model contains their
activities (underwriting, claim settlement, reserving, reinsurance,
investing, and other), accounting and reporting elements (asset, equity,
insurance reserve, and liability stocks), as well as financial health
indicators.
The behavior of the built model is largely determined by the
feedback effects of the main reinforcing and balancing loops.
18
Insurance rate has a double-sided effect on the company’s financial
performance: on the one hand, its growth provides higher revenues, but
on the other hand, market demand may fall due to an extremely high
relative insurance rate. Additionally, when insurance revenues rise,
insurance rate drops because of the adjustment effect, which brings it to
the loss level.
Free funds and reserve investing have a reinforcing influence on
profitability and equity dynamics. Investing more cash means more
investment income and more funds available for investing in the next
period. This feedback effect largely determines the growth possibilities
for general insurers.
Other major loops characterize the importance of reinsurance on
company performance: on the one hand, ceding premiums can reduce the
payout pressure on the insurer; on the other hand, using reinsurance
deprives insurers of a part of eamed premiums.
Testing of feedback effects presented in the model has shown that
they can be utilized in management practice as a means of affecting the
financial condition of the insurer.
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19
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Data sources:
National Commission for Regulation of Financial Services Markets of
Ukraine (NCRFSM): http://nfp.gov.ua
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http://etalon.ua
20
Appendix
Equation excerpts for selected modules
J eiaarial Relative Reserving Perjéd change in RUPR
Ae) ~O
Figure A 1. Stock-flow diagram of Underwriting module
Equations:
Average_insurance_sum_per contract = Market insurance sum_per_contract
Brand_INPUT_FROM_MARKETING =1
Contracts_signed =
min(Human_resources.Sales_capacity,Number_of_contracts_based_on_demand)
Demand _ for the company's services =
Demand _ for the company's services normal*Effect_of_brand_on_demand*Effect_
of_relative_insurance_rate_on_demand
Demand_for the company's_services_normal = 1000000
Desired_share of insurance sum to_be reinsured =0
Effect_of_brand_on_demand = Brand_INPUT_FROM_MARKETING
Effect_of_relative insurance rate on_demand =
smth1(1/Actuarial.Relative _insurace_rate,1)
Gross _insurance premiums written =
Contracts_signed*Average_insurance_sum_per_contract*Actuarial.Gross__insuranc
e rate
Market_insurance_sum_per contract = 1000+step(4000,10)*0
Net_insurance premiums earned =Gross insurance premiums _written-
Reinsurance.Insurance_premiums ceded-
Reserving.Cash_UPR_reserving_and_reserve_returning+Reserving.Period_change i
n_RUPR
Number of contracts based_on_demand =
Demand _for the company’'s_services/Average_insurance_sum_per_contract
21
Share_of_insurance_sum_to_be_reinsured =
(max(0,(Average_insurance_sum_per contract-
Reinsurance.A llowed_retention)/Average_insurance_sum_per_contract))
laims Period Waurgnce os
payouts outstandi
ci
Figure A 2. Stock-flow diagram of Reinsurance module
Equations:
Payments _to_reinsurers_backlog(t) = Payments_to_reinsurers_backlog(t - dt) +
(Change_in PRB) * dt
INIT Payments _to_reinsurers backlog =0
INFLOWS:
Reinsurer operations profit = Insurance premiums _ceded-
Insurance_payouts_compensated
Reinsurer_profit_received =
max(0,Reinsurer operations profit)*Share_of_reinsurer_profit_paid_to_cedent
Share_of_reinsurer_profit_paid_to_cedent =0
Change_in PRB = Insurance premiums ceded-Cash.Insurance_premiums_ceded
Allowed_retention = (IF ((Equity.RE_or AL+Equity.Paid_in_capital)>=0) THEN
max(0,(Insurance_reservest+Equity.RE_or AL+Equity.Paid_in_capital)*Allowed_sh
are_of_premiums to_net_assets) Else 0)*0
+max(0,(Insurance_reservestEquity.RE_or AL+Equity.Paid_in_capital)*Allowed_s
hare of premiums to_net_assets)
Allowed_share_of premiums to_net_assets = 0.1
Ceding fee received =0
Insurance_payouts_compensated =
Claims.Period_insurance_payouts_outstanding*Underwriting.Share_of_insurance_su
m_to_be reinsured
22
Insurance_premiums ceded =
Underwriting.Gross_insurance__premiums_written*Underwriting.Share_of_insuranc
e sum _to_be reinsured
Insurance_reserves =
Reserving.Total__equalization_reserve+Reserving.Unearned_premium_reserve+Rese
rving.Total_ IBNR_claims reserve+Reserving.Total_ RBNS claims reserve
Other reinsurance _related_revenues =
Ceding _fee_received+Reinsurer_profit_received
K
cash ourance and
wi te
——
\
Underwriting Contracts signed
\ tie
contacts
ce payet
Figure A3. Stock-flow diagram of Claims module
Equations:
Accounts__payable(t) =Accounts__payable(t - dt) + (Accounts_payable_adjustment)
* dt
INIT Accounts payable =0
INFLOWS:
Accounts payable_adjustment = Period insurance payouts _outstanding-
Cash.Insurance_and_reinsurance_payouts
Active__contracts(t) =Active__contracts(t - dt) + (Contract_signing -
Contract_expiry - Contract_realization) * dt
INIT Active__contracts = Average _insurance__contract_term*Contract_signing
INFLOWS:
Contract_signing = Underwriting.Contracts_signed
23
OUTFLOWS:
Contract_expiry =Active__contracts/Average_insurance__contract_term-
Contract_realization
Contract_realization = Insurance_risk*(1-Claim_denial__share)*Active contracts
Contracts_waiting__ for payouts(t) =Contracts_waiting__for payouts(t - dt) +
(Contract_realization - Contract_settlement) * dt
INIT Contracts waiting for payouts =0
INFLOWS:
Contract_realization = Insurance_risk*(1-Claim_denial__share)*Active__ contracts
OUTFLOWS:
Contract_settlement =
Cash.Insurance_and_reinsurance_payouts/Average_claim__sum_trimmed
Expired__contracts(t) = Expired__contracts(t - dt) + (Contract_expiry) * dt
INIT Expired__contracts = 0
INFLOWS:
Contract_expiry =Active__contracts/Average_insurance__contract_term-
Contract_realization
Settled__contracts(t) = Settled__contracts(t - dt) + (Contract_settlement) * dt
INIT Settled__ contracts =0
INFLOWS:
Contract_settlement =
Cash.Insurance_and_reinsurance_payouts/Average_claim__sum_trimmed
Average_claim_sum =
smth1(Underwriting.A verage_insurance sum_per contract*1.2,1)
Average claim _sum_trimmed =
min(Underwriting.Average_insurance_sum_per_contract,Average_claim_sum)
Average insurance _contract_term =4
Claim_denial__ share = 0.25
Claim_sum_reported =Average claim__sum_trimmed*Contract_realization
Fraction_of_liquidation_costs_in claim_sum =0.001
Insurance_risk = 0.05
Liquidation_costs =
Claim_sum_reported*Fraction_of_liquidation_costs_in_claim_sum
Period_insurance_payouts_outstanding =
Contract_realization*Average_claim__sum_trimmed
Total_insurance payouts outstanding =
Period insurance payouts outstanding+Accounts__ payable
24
@
Le
Gani fii
Oe,
deneeting Averige ra =
insurance sum por contract te )
race Risk Perum —
cs —- an Time to adjust
S| \ Pa poo, GE ota
Underwriting Contracts signed \ iets 2 Cocca: SX, Cy
\ “a insurance rato Sy UA
fe \ we
\ / craion neue ee
late Pete earanee / eine
payouts outstanding /
at
cy “ costs |
iio ai ae
kab cove mane
Liguidaten costs
Clatins Liquidation costs
average merect
insurance rate
Figure A 4. Stock-flow diagram of Actuarial module
Equations:
Gross__insurance_rate(t) =Gross__insurance_rate(t - dt) +
(Change_in_gross_ insurance rate) * dt
INIT Gross__insurance_rate = 100*0.15/(100-0.265-24.735)
INFLOWS:
Change_in_gross_insurance_rate =(Indicated_gross__insurance_rate-
Gross__insurance_rate)/Time_to_adjust_insurance_rate
Acquisition_costs =
Human _resources.Variable__marketing_costs*Share_of acquisition costs_in_variab
le_marketing_costs/Total_insurance_sum_of_insured_objects*100
Average market insurance _rate =0.2
Case_conduction_costs = Acquisition_costs+Liquidation_costs
Indicated_gross__insurance_rate = 100*Net_insurance_rate/(100-
Case_conduction_costs-Planned_pofitability)
Liquidation_costs =
Claims.Liquidation_costs/Total_insurance_sum_of_insured_objects*100
25
Net_insurance_rate =
(Claims.Period_insurance_payouts_outstanding/Total_insurance_sum_of_insured_ob
jects+Risk_premium)
Planned_pofitability = 24.735
Quantile_of_risk =0
Relative _insurace_rate =Gross__insurance_rate/Average_market__insurance_rate
Risk_premium = 1.2*Quantile_of_risk
Share_of_acquisition_costs_ in variable_marketing_costs =0.1
Time_to_adjust_insurance_rate = 1
Total_insurance_sum_of_insured_objects =
Underwriting.Average_insurance_sum_per contract*Underwriting.Contracts_signed
On L O
ia eran Fa ly, Freed sostsFiced oe eo
he asset purchases, g incoate and kept sociel tax
CClatms.Liquidation costs
Costs and expanses fax payment
cb
Insurance pramiume wriaon ~~~ __ stance a veinirrce intr pecan ecel cs premiums coded
Cox con
Reinsurance insurance &.
coon
a” Insurance and cn
> tine Fy. Claims.Total insurance
valine te =
a Reserving UPR Se aa
ee Led
per 29 See
eee a
Resorving. Total veh ij Reserving Reported bar not
rig ot / =
4 ? Resening IBNR neha
SL/) J i
eee | ees ae
fe! P if Reserang ER ee
Reserving. Totaf't if Reserving.Equalization
ae
Reserving. Tofal ER
Investing pesult
Fixed asset. Fixed asset sales
Figure A5. Stock-flow diagram of Cash module
Equations:
Cash(t) = Cash(t - dt) + (Insurance_and_reinsurance_premium_revenues +
Other revenues or losses - Insurance_premiums ceded - Tax_payment -
Reserving_UPR - Reserving RBNS - Reserving_IBNR - Reserving_ER -
26
Costs_and_expenses - Insurance_and_reinsurance_payouts - Investing_and_returning
- Fixed_assets_purchases) * dt
INIT Cash =
Costs_and_expenses+Fixed_assets_purchases+Tax_payment+Insurance_premiums_c
eded+nsurance_and_reinsurance_payouts+Reserving_IBNR+Reserving ER+Reserv
ing_RBNS+Reserving_UPR
INFLOWS:
Insurance_and_reinsurance_premium_revenues =
Underwriting.Gross insurance premiums written
Other revenues or losses =
(Fixed__assets.Fixed_asset_sales+Investing.Total__investing_result+Reserving.T otal
_UPR__investing_result+Reserving.T otal RBNS__ investing result+Reserving.T otal
_IBNR__ investing _result_2+Reserving.Total_ER__investing_result+Reinsurance.Ot
her_reinsurance_related_revenues)+Reinsurance.Insurance_payouts compensated
OUTFLOWS:
Insurance_premiums_ ceded = Reinsurance.Insurance_ premiums ceded
Tax_payment =
Tax_calculation.Total_tax_to_be paid+Human_resources.Salary_ income and kept_
social_tax
Reserving UPR =Reserving.Unearned_premium__reserve_gap
Reserving RBNS = Reserving.Reported_but_not_settled_claims reserve_gap
Reserving_IBNR = Reserving.Incurred_but_not_reported_reserve_gap
Reserving_ER = Reserving.Equalization_reserve_gap
Costs_and_expenses = Human_resources.Total_costs+Claims.Liquidation_costs
Insurance_and_reinsurance_payouts = Claims.Total_insurance_payouts_outstanding
Investing_and_returning = Investing. Investing _and_retumming
Fixed_assets_purchases = Fixed__assets.Fixed_asset_purchases
QO O
Q Tax calculation Period tax
Paid in
capital
i
Fixed assets.Fixed wy
asset oo te /e
Reinsurance.lnsurance, i.
premiums ceded \
ry a \ Required paid in
Human resources. PeriogtCosts me 3 \
oot és Ci N
—)
payouts outst st
Ny ND Equity additions
Claims.Liquidation costs Cash. a sf Reser change in RUPR
Cash.Reservifig RBNS Reserving Pe 2 chenge in RRBNS
Cash.Reserving ER Cash. Reserving UPR
Figure A6. Stock-flow diagram of Equity module
Equations:
Equity(t) = Equity(t - dt) + (Equity_additions - Equity_withdrawal) * dt
INIT Equity = Paid_in_capital
INFLOWS:
Equity_additions = Paid_in_capital_additions+Profit_or_loss-Tax
OUTFLOWS:
Equity_withdrawal = Dividend_decision
RE_or AL(t) =RE_ or AL(t- dt) + (Profit_or_loss - Tax) * dt
INIT RE_or AL =0
INFLOWS:
Profit_or_loss =-
Fixed__assets.Fixed_asset_depreciation+Cash.Insurance_and_reinsurance_premium_
revenues+Cash.Other_revenues_or_losses-
Claims.Period insurance payouts _outstanding-Human_resources.Period_costs
-Reinsurance.Insurance_premiums_ceded-Claims.Liquidation_costs-
Total_reserving_results
OUTFLOWS:
Tax =Tax_calculation.Period_tax
Paid_in_capital(t) = Paid_in_capital(t - dt) + (Paid_in_capital_additions) * dt
28
INIT Paid_in_capital = Required_paid_in_ capital
INFLOWS:
Paid_in_capital_additions =(Required_paid_in_capital-Paid_in_capital)
Dividend_decision = 0
Required_paid_in_capital = 1000000
Total_reserving_results =
Cash.Reserving_IBNR+Cash.Reserving RBNS+Cash.Reserving UPR+Cash.Reservi
ng_ER-Reserving.Period_change in RUPR-Reserving.Period change in RRBNS
