Finance and Credit
 

An economic and mathematical model to calculate the insurance tariffs of partners

Vol. 23, Iss. 32, AUGUST 2017

Received: 18 May 2017

Received in revised form: 9 June 2017

Received in final form: 7 July 2017

Accepted: 25 July 2017

Available online: 29 August 2017

Subject Heading: Insurance

JEL Classification: C02

Pages: 1944–1954

https://doi.org/10.24891/fc.23.32.1944

Chistyakova N.A. Plekhanov Russian University of Economics, Moscow, Russian Federation chistna@mail.ru

Sukhorukova I.V. Plekhanov Russian University of Economics, Moscow, Russian Federation suhorukovaira@yandex.ru

Subject The article addresses actuarial system of control and management in the sphere of risk insurance.
Objectives The purpose of the article is to provide methodological justification and develop an economic and mathematical model to calculate net rate of insurance coverage payment to a partner (living spouse) in the event of death of another partner (spouse) prior to his/her retirement age.
Methods We use the actuarial techniques of calculating insurance tariffs based on mathematical and simulation methods. The paper presents an economic and mathematical model to calculate insurance tariffs for personal life insurance, assuming that the insured are spouses and one of them is a beneficiary. The calculations rest on methods of the theory of probability, actuarial mathematics, numerical methods and methods of simulation modeling, when required.
Results We offer an analytical form of the rate of insurance coverage payment to a living partner in the event of death of another prior to his or her retirement age. It depends on interest rate, age of spouses, remaining time before pension, mortality rate, and maximum permissible age. We also calculated the probability of obtaining insurance coverage by each of the partners and the value of the contract (mathematical expectation of insurer's costs) at the contract date.
Conclusions The findings enable to obtain analytical forms for probability of joint project termination as a result of the other partner's actions, as well as for calculating insurance tariffs in the form of one-off payment.

Keywords: insurance tariff, net rate, whole life insurance policy, interest rate, survival function

References:

  1. Falin G.I. Matematicheskie osnovy teorii strakhovaniya zhizni i pensionnykh skhem [Mathematical foundations of the theory of life insurance and pension schemes]. Moscow, Ankil Publ., 2002, 262 p.
  2. Chistyakova N.A. [Calculating the probabilities in the model of life insurance of spouses]. Nauchnye trudy vol'nogo ekonomicheskogo obshchestva Rossii. Materialy 4-i Mezhdunarodnoi nauchno-prakticheskoi konferentsii im. A.I. Kitova “Matematicheskie metody i informatsionnye tekhnologii v ekonomike i upravlenii” [Proc. A.I. Kitov 4th Int. Sci. Conf. Mathematical Methods and Information Technologies in Economics and Management]. Moscow, Plekhanov Russian University of Economics Publ., 2014, pp. 148–151.
  3. Chistyakova N.A. [The cost of contract in the model of co-insurance of spouses]. Izvestiya Rossiiskogo ekonomicheskogo universiteta im G.V. Plekhanova, 2015, no. 3, pp. 250–254. (In Russ.) URL: https://elibrary.ru/item.asp?id=25597710
  4. 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. 918–926. (In Russ.)
  5. 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.)
  6. Kurganov V.V., Tsyganov A.A. [The Russian practice of liability insurance of persons involved in construction oversight]. Rossiiskoe predprinimatel'stvo = Russian Journal of Entrepreneurship, 2016, vol. 17, no. 16, pp. 1975–1990. (In Russ.)
  7. Burak V.E. [Calculation of costs of measuring the working environment factors during special assessment of labor conditions]. Ekonomika truda = Russian Journal of Labor Economics, 2015, vol. 2, no. 3, pp. 145–154. URL: https://elibrary.ru/item.asp?id=25640123 (In Russ.)
  8. Zolotareva V.P. [The role of insurance in acceleration of investment processes in the post-reform Russia]. Rossiiskoe predprinimatel'stvo = Russian Journal of Entrepreneurship, 2016, vol. 17, no. 7, pp. 919–930. (In Russ.)
  9. Bowers N.L., Gerber H.U., Hickman J.C., Jones D.A., Nesbitt C.J. Actuarial Mathematics. 2nd Edition. The Society of Actuaries, 1997, 730 p.
  10. Gantenbein M., Mata M.A. Swiss Annuities and Life Insurance: Secure Returns, Asset Protection, and Privacy. Wiley, 2008, 332 p.
  11. Panjer H.H., Pedersen H.W. Financial Economics: With Applications to Investments, Insurance, and Pensions. RECORD, 1997, vol. 23, no. 2, pp. 1–6.
  12. Kaas R., Goovaerts M., Dhaene J., Denuit M. Modern Actuarial Risk Theory. Kluwer Academic Publishers, 2001, 309 p.
  13. Olivieri A., Pitacco E. Introduction to Insurance Mathematics: Technical and Financial Features of Risk Transfers. Springer, 2011, 490 p.
  14. Black K.Jr., Skipper H.D., Black K.III. Life Insurance. 14th ed. Lucretian, LLC, 2013, 736 p.
  15. Dubovskikh K.I., Smirnova A.A., Trofimova V.Sh. [Application of mathematical statistics in actuarial calculations]. Prilozhenie matematiki v ekonomicheskikh i tekhnicheskikh issledovaniyakh = The Application of Mathematics in Economic and Technical Studies, 2014, no. 4, pp. 82–86. (In Russ.)
  16. Boikov A.V. [Insurance: Actuarial calculations and mathematical models of insurance]. Aktuarii = Actuary, 2009, no. 1, p. 35. URL: https://elibrary.ru/item.asp?id=28847635 (In Russ.)
  17. Ryabikin V.I., Tikhomirov S.N., Baskakov V.N. [Insurance and actuarial calculations]. Aktuarii = Actuary, 2007, no. 1, p. 26. URL: https://elibrary.ru/item.asp?id=28847570 (In Russ.)
  18. Sinyavskaya T.G., Tregubova A.A. [Regional risk of individual life insurance: Approaches to assessment and management of tariffs]. Uchet i statistika = Accounting and Statistics, 2015, no. 3, pp. 54–61. (In Russ.)

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