Optimal control of continuous life insurance model

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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.

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    • 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)