Gompertz–Makeham parameter estimations and valuation approaches: Turkish life insurance sector

For participating life insurance, the objective of insurance companies is to control the investments of policyholders by considering changing market conditions within the scope of risk management and increase their returns. Given that insurance companies compete in the market with participating life insurance, insurers and academicians attempt to develop this product. This paper compares net premium valuation and paid-up valuation methods used in the valuation of participating life insurance contracts in Turkey. The development of a single endowment policy with a level premium payment has been modeled as a time-continuous Markov chain model. Mortality in Turkey has been determined by calculating the parameter values of the Gompertz–Makeham function. It has been observed that insurance companies would not face valuation losses using the paid-up valuation method, even though policyholders stopped premium payments before the policy term. Moreover, compared with other valuation methods, the paid-up valuation method has been found to offer freedom of investment.