TERM LIFE INSURANCE PRICING WITH STACKELBERG GAME THEORY

• Main Author: CLARISSA, MARGARETH
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/65403
• Institution: Institut Teknologi Bandung

Premium calculation with the equivalence principle only considers one party, namely the insurance company (the insurer), while the policyholder (the insured) is not involved. This can make the specified premium doesn’t take into account the insured’s utility, so it is possible for the insured to reject the proposed policy. Therefore, a model is needed to involve both the insurer and the insured in the premium calculation. Game theory can help insurance companies to include information other than risk in determining premiums. In this final project, the calculation of life insurance premium is modeled by applying game theory, which is based on the two-player Stackelberg Game. The two players are the insures as the leader and the insured as the follower. In this final project, the insurer offers 2 (two) policy strategies (????), namely Policy A (????=1) and Policy B (????=2). Both are 10-years term life insurance products with premiums ????1, ????2 and benefits 0,01????12, 0,02????22. Meanwhile, the insured also has 2 (two) strategies (????), that is to reject (????=0), or accept (????=1) the proposed policy. Initially, the premium of each policy will be determined by finding the values of ????1 and ????2 that maximize the objective functions of the insurer, namely the expected profit of the insurer, analytically and by genetic algorithms. Then, the premium values will be used to calculate the expected profit of the insured. Finally, the game solution will be determined based on the backward induction method. Conditional to the insured at the age of 45 years old, the value of ????1 is $6.791,225 and ????2 is =$3.395,613 with the benefits $461.207,37 and $230.603,75. The analytical result is the same with using genetic algorithm. The insured’s expected profit if they does not propose any policy is $0 and if they offer Policy A and Policy B are $17.097,86 and $8.548,929, respectively. As for the insured, the expected profit if they reject the proposed policy, accept Policy A or Policy B are $93.179,67,$382.985,40 ???????????? $267.703,10, respectively. Thus, the optimal solution to the game problem is that the insurer offers Policy A and the insured accepts the policy offer.