Subject The article addresses the calculation of optimal indices of insurance reserves when regulating and managing the process of joint commercial activity of several partners in the event of early termination of business by either party due to external circumstances. Objectives The aim is to substantiate the actuarial method of calculation and the working formulas for calculation of mathematical reserve under insurance contracts with several insured parties, providing a balanced solution to social and economic problems and insurance portfolio sustainability. Methods We employed probability-theoretical methods of work with vector-type random values and characters, and actuarial models for mathematical reserve calculation. Results The paper provides a scientific and methodological substantiation and presents an economic and mathematical model to calculate reserves for coinsurance contracts that are exposed to the risk of early termination of business by either party due to external circumstances. We obtained working formulas for calculation of mathematical reserve at any time during the term of the contract, formulated scientific and practical recommendations on coinsurance of commercial activity of several partners if faced with early termination by either party due to external circumstances. Conclusions The findings show that the developed methodology can be applied to both a certain type of insurance product and to contracts that include different types of insurance products. This will enable to increase the liability of insurance companies for the implications of their tariff policy. The offered methods allow to consider possible risks at all stages of decision-making and avoid adverse economic effect in the business.
Keywords: insurance tariff, net rate, distribution density, distribution function, economic and mathematical model of risk insurance
Larionov A.V. [The role of the Bank of Russia in risk management of insurance companies]. Finansy i kredit = Finance and Credit, 2018, vol. 24, iss. 3, pp. 679–690. (In Russ.) URL: Link
Kuldashev K.M. [The insurance market of Uzbekistan and the need to create mutual insurance companies]. Ekonomicheskii analiz: teoriya i praktika = Economic Analysis: Theory and Practice, 2018, vol. 17, iss. 4, pp. 690–703. (In Russ.) URL: Link
Kogdenko V.G. [Specifics of analysis of companies operating in the digital economy]. Ekonomicheskii analiz: teoriya i praktika = Economic Analysis: Theory and Practice, 2018, vol. 17, iss. 3, pp. 424–438. (In Russ.) URL: Link
Laptev P.V. [The global trend of social security in Europe: Raising the retirement age]. Kreativnaya ekonomika = Journal of Creative Economy, 2015, vol. 9, no. 7, pp. 917–926. URL: Link (In Russ.)
Vedmed' I.Yu., Vorontsov D.N. [Influence macroeconomic indicators for the insurance premium]. Strakhovoe delo = Insurance Business, 2017, no. 3, pp. 39–43. (In Russ.)
Black K. Jr., Skipper H.D., Black K. III. Life Insurance. Lucretian, LLC, 2013, 736 p.
Olivieri A., Pitacco E. Introduction to Insurance Mathematics: Technical and Financial Features of Risk Transfers. Springer, 2011, 490 p.
Gantenbein M., Mata M.A. Swiss Annuities and Life Insurance: Secure Returns, Asset Protection, and Privacy. John Wiley & Sons, Inc., 2008, 332 p.
Vlasov D.A., Sinchukov A.V. [Research of game-theoretic models of decision-making under competitive conditions]. Konkurentosposobnost' v global'nom mire: ekonomika, nauka, tekhnologii = Competitiveness in a Global World: Economics, Science, Technology, 2017, no. 10, part 5, pp. 692–695. URL: Link (In Russ.)
Sinyavskaya T.G., Tregubova A.A. [Individual life insurance regional risk: Approaches to estimating and calculating insurance rates]. Uchet i statistika = Accounting and Statistics, 2015, no. 3, pp. 54–61. URL: Link (In Russ.)
Sukhorukova I.V., Chistyakova N.A [Calculation of the term of the joint insurance of partners (spouses)]. Innovatsionnoe razvitie ekonomiki = Innovative Development of Economy, 2017, no. 4, pp. 173–177. URL: Link (In Russ.)
Sukhorukova I.V., Chistyakova N.A. [Actuarial calculation of companion insurance tariffs]. Plekhanovskii nauchnyi byulleten', 2018, no. 1, pp. 105–110. (In Russ.)
Chistyakova N.A., Sukhorukova I.V. [An economic and mathematical model to calculate the insurance tariffs of partners]. Finansy i kredit = Finance and Credit, 2017, vol. 23, iss. 32, pp. 1944–1954. (In Russ.) URL: Link