DETERMINING THE NET PREMIUM MODEL THROUGH GT(2)- GA (GAME THEORY TWO-PLAYERS-GENETIC ALGORITHM) CASE STUDY: FIRE INSURANCE DATA

• Main Author: Ikhsan Kalla, Muhammad
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/63902
• Institution: Institut Teknologi Bandung

Indonesia's uneven population density makes a densely populated area with a high risk of fire hazards. For example, the first population density reaches 15,978 people/km2 (DKI Jakarta Province), whereas Indonesia's population density is only 142 people/km2 (BPS, 2021). Based on data from the DKI Jakarta Provincial Fire Department, throughout 2020, there were 1505 fire incidents, with losses reaching Rp. 252,057,901,000. Unfortunately, fire insurance is still not much in demand by the public compared to general insurance (e.g., vehicles) and life insurance (mediaindonesia.com). Since residential, warehouse, and office assets have a very high value, it is crucial to protect them so that the owner (the insured) is free from losses due to damage or destruction that occurs randomly. This thesis research begins by analyzing fire data in Indonesia in 2006-2016, occupancy 2927 and 2937. There are a total of 388 claims with three types of coverage; (i) buildings (179 claims), (ii) stock and content (126 claims), and (iii) buildings, stock and content (83 claims). Information on the distribution fitting results of the three types of coverage will be used to estimate the optimal net premium value of the model built. Generally, premium modeling uses the conventional method, which only involves one party (the insurer) without the insured. In fact, setting a premium that is too large allows the product to be rejected by the insured, and conversely, a toosmall premium allows the insurer to fail to pay the claim. Therefore, this study will consider the insured in estimating the net premium value through the two-player game theory (GT(2)) Stackelberg formulation. The insurer, as the leader, offers 3 (three) fire insurance products: policy A (building), B (stock and content), and C (building, stock, and content). Furthermore, as a follower, the insured will decide to accept or reject the product offer. The insurer's decision will be based on the maximization of the profit function ( ) which is the difference between income and expenditure on the strategy chosen by the insured. While the insured profit ( ) is modeled using the exponential utility function, ( ) ( ) and the natural logarithm, ( ) ( ) for assuming risk aversion. Furthermore, the optimization of the premium value on the two profit functions of each player is carried out using the Genetic Algorithm (GA). GA is a method of optimizing the value of a function by utilizing a natural selection process known as the evolutionary process, which includes inheritance, natural selection, crossover, and mutation. The result of this research is the optimal premium interval for A, B, and C policy for each utility function. Optimal premium for A, B, and C policy with (i) exponential utility function are (0.799043, 0.826065) billion, (1.491276, 1.498457) billion, and (1.298029, 1.300866) billion, respectively, and with (ii) natural logarithm utility function are (0.741696, 0.754026) billion, (1.064551, 1.251490) billion, and (0.900665, 0.925279) billion, respectively. The best scenario that maximizes each party's profit is (i) the insured party's exponential utility function, with the insurer offering policy C at the interval (1.298029, 1.300866) billion, and (ii) the insured party's natural logarithm utility function, with the insurer offering policy B at the premium interval (1.064551, 1.251490) billion. The optimal scenario is using (i), with a profit interval of (0.96427, 0.96711) billion for the insurer and (0.96286, 0.96427) billion for the insured.