Optimal control of continuous life insurance model
-
DOIhttp://dx.doi.org/10.21511/imfi.14(4).2017.03
-
Article InfoVolume 14 2017, Issue #4, pp. 21-29
- Cited by
- 1959 Views
-
217 Downloads
This work is licensed under a
Creative Commons Attribution-NonCommercial 4.0 International License
The problems of mixed life insurance and insurance in the case of death are considered in the article. The actuarial present value of life insurance is found by solving a system of differential equations. The cases of both constant effective interest rates and variables, depending on the time interval, are examined. The authors used the Pontryagin maximum principle method as the most efficient one, in order to solve the problem of optimal control of the mixed life insurance value. The variable effective interest rate is considered as the control parameter. Some numerical results were given.
- Keywords
-
JEL Classification (Paper profile tab)C58, C61, G20, G22
-
References24
-
Tables0
-
Figures8
-
- Figure 1. Distribution of the present actuarial value of benefits for the case of mixed life insurance
- Figure 2. Distribution of the present actuarial value of benefits for the case of death
- Figure 3. Distribution of the present actuarial value of benefits for the case of mixed life insurance.
- Figure 4. Distribution of the present actuarial value of benefits for the case of death
- Figure 5. Finding the switching point of control problem (i = 0.01)
- Figure 6. Distribution of the present actuarial value of benefits for the case of mixed life insurance (i = 0.01)
- Figure 7. Finding the f switching point of control problem (Option B)
- Figure 8. Distribution of the present actuarial value of benefits for the case of mixed life insurance (Option B)
-
- Arutyunov, A. V., Magaril-Il’yaev, G. G., Tihomirov, V. M. (2006). Pontryagin Maximum Principle. Proofs and applications (144 p.). Moscow: Univ. Factorial Press.
- Bazilevich, V. D. (2008). Insurance (1019 p.). Znannya, K.
- Biagini, F., Botero, C., Schreiber, I. (2017). Risk-minimization for life insurance liabilities with dependent mortality risk. Mathematical Finance, 27(2), 505-533.
- Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A., Nesbitt, C. J. (1997). Actuarial mathematics (2nd ed.). The Society of Actuaries.
- Campbell, R. A. (1980). The Demand for Life Insurance: An Application of the Economics of Uncertainty. Journal of Finance, 35, 1155-1172.
- Chen, R., Wong, K. A., Lee, H. C. (2001). Age, Period and Cohort Effects on Life Insurance Purchases in the U.S. Journal of Risk and Insurance, 68, 303-327.
- Cox, S. H., Hogan, A. M. B. (1995). Life Insurer Risk-Based Capital: An Option Pricing Approach. Journal of Actuarial Practice, 3(1), 5-23.
- D’Ortona, N. E., & Staffa, M. S. (2016). The theoretical surrender value in life insurance. Insurance Markets and Companies, 7(1).
- Engsner, H., Lindholm, M., Lindskog, F. (2017). Insurance valuation: A computable multi-period cost-of-capital approach. Insurance: Mathematics and Economics, 72, 250-264.
- Gaillardetz, P., Lakhmiri, J. Y. (2011). A New Premium Principle for Equity-Indexed Annuities. The Journal of Risk and Insurance, 78(1), 245-265.
- Gerber, H. U. (1997). Life Insurance Mathematics (217 p.) (3d ed.). Springer.
- Hampton, J. J. (1993). Financial Management of Insurance Companies (219 p.). AMACOM. American Management Association.
- Huang, H., Milevsky, M. A., Wang, J. (2008). Portfolio Choice and Life Insurance: the CRRA Case. The Journal of Risk and Insurance, 75(4), 847-872.
- Jung, A., Mongelli, F. P. (2016). Monetary policy decision-making when information search is costly. Banks and Bank Systems, 11(1), 15-22.
- Kozmenko, O. V., Kozmenko, S. M., Vasilieva, T. A. (2014). “4P” Marketing Insurance (432 p.). University Book, Sumy.
- Kurylo, V., Kurylo, L., Zhovnirchyk, Ya., Kartashov, Ye., & Sokol, S. (2017). The development of the insurance market of Ukraine amid the global trends in insurance. Investment Management and Financial Innovations, 14(1-1), 211-216.
- Lewis, F. D. (1989). Dependents and the Demand for Life Insurance. American Economic Review, 79, 452-467.
- Li, D., Moshirian, F., Nguyen, P., Wee, T. (2007). The Demand for Life Insurance in OECD Countries. The Journal of Risk and Insurance, 74(3), 637-652.
- Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., Mishchenko, E. F. (1983). The Mathematical Theory of Optimal Processes (392 p.). Nauka.
- Porrini, D. (2017). Regulating Big Data effects in the European insurance market. Insurance Markets and Companies, 8(1), 6-15.
- Russo, V., Giacometti, R., Fabozzi, F. J. (2017). Intensity-based framework for surrender modeling in life insurance. Insurance: Mathematics and Economics, 72, 189-196.
- Shell, K. (1969). Application of Pontryagin’s Maximum Principle to Economics. Mathematical System Theory and Economics. Leet. Notes Oper. Res. and Math. Econ. 11(241-292). Springer, Berlin.
- The AnyLogic Company.
- Trynchuk, V. (2017). Management of visual communications in insurance companies (on the example of using icons in logos). Problems and Perspectives in Management, 15(2-2), 319-331.