Stackelberg Equilibrium Between the Insured and the Insurer in n-Year Life Insurance for Maximizing Profit

In the life insurance industry, determining the amount of premium paid by the insured to the insurer is crucial. This paper uses Stackelberg’s game theory to describe the reality that occurs between two parties involved in this business, i.e. the insured and the insurer. The insurer as a leader offers four different insurance products, and the insured as a follower has two strategies: (1) accepting or (2) rejecting one of the offered insurance products. The amount of premium is obtained by optimizing the insurer’s profit for each insurance product and the insured’s choice of strategy with a certain premium value limit. For the model formulation, the Indonesia Mortality Table IV is used as a guide to obtaining the parameters of the Makeham and Gompertz distribution (survival) functions. The developed model can determine (1) the amount of premium for each insurance product offered, (2) the expectation of insureds who will purchase each insurance product, and (3) the maximum profit for each of the two parties. A genetic algorithm is used to obtain the best solution. The result shows that the third insurance product, which uses Makeham distribution and offers two types of benefits, is preferred by the two parties involved.