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Abstract
In the context of the stochastic models for the management of life insurance portfolio, the authors explore, with simulation approach, the effects induced by the application of a particular method of calculation of the surrender value. In the life insurance, the policyholder position is, at any moment, quantified by the mathematical reserve. In case the reserve amount results are positive, the insurance company can allow the contract surrender, consisting in an amount payment, called surrender value, commensurate with the mathematical reserve. Generally, the insurance company enforces some restrictions in the surrender value determination, in order to avoid, first of all, that an amount is disbursed to the policyholder while, on the contrary, he results to be indebted to the Company. In this paper the authors will consider a surrender value calculation method based precisely on the profit recovery concept which shall be supplied by the contract in case it remains in the portfolio. Additionally, the authors shall analyze, by simulation approach, the effects caused by the enforcement of the surrender value calculation concept on a life portfolio profitability, and on the penalties extent enforced to the policyholders which cancel from the contract. Keywords: surrender value, life insurance, internal risk model, stochastic simulation
Highlights
In the life insurance relationship, the policyholder position is, at any moment, quantified by the mathematical reserve
The insurance company enforces some restrictions in the surrender value determination, in order to avoid, first of all, an amount is disbursed to the policyholder while, on the contrary, he results to be indebted to the company
Other surrender value restrictions are due to the penalty enforcement, for the reason of the insurance company requirement to recover those future profits whose progressive formation is interrupted by the surrender
Summary
The insurance profit of an insurance company operative in the life business originates from the handling of policies forming the portfolio, and it is originated by the deviation between predictions assumed in the premiums calculation and the real experience. Bt+1 = bt+1 wt st+1 Qt is the expense-loaded premium paid by the policyholders at beginning of period (delays aren’t predicted on the payment of the same and, the credits towards policyholders for premiums aren’t considered); the amount is attained enforcing the premium rate bt+1 , relevant to the generation insurance contract, to the total capitals insured wt net of the capitals relevant to policies self-deleted (at the year beginning) for elapses st+1. X t+1 = xt+1Qt is the accidents amount happened during the financial period, all of them paid as a possibility at the year end (there will not be available any reserve for amounts to be paid); it depends, such as for the reserves rates vtband for the premiums bt+1, from the generation insurance contract.
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