Compound binomial risk model in a Markovian environment with capital cost and the calculation algorithm

Abstract

The operation of insurance institution is often affected by random environment, potential opportunity cost of capital or inflation. Considering this phenomenon, this paper establishes a new Markovian environment compound binomial risk model with capital cost, abbreviated as RMCM model. The new RMCM model is a complex recursive model which is difficult to calculate. To calculate the results in many future periods at one time, it is necessary to design an algorithm that can greatly improve calculation efficiency. One of the aims of this study is to conduct an analysis of the recursive algorithm, divide and conquer strategy and other algorithm theories to, designs a new MCPRAM-algorithm that is able to solve the calculation of this kind of recursive model with high complexity, multiple cycles and multiple periods, significantly improving the practical application value of the actuarial model. Taking aviation accident insurance as an example, the measurement methods of actuarial quantity in the model are explained statistically, and the calculation algorithm of conditional ruin probability is elaborated in detail. The conditional ruin probabilities of 60 periods under different operating conditions and different environment states were obtained and then compared and analyzed. RMCM has a wide range of applications and is suitable for describing the insurance products with low premium, small compensation probability; large claim amount and one-off compensation in a random market environment. The RMCM model proposed in this paper clarifies the risk of insurance institutions, compares the calculation of seven groups of parameter data, and obtains better parameters to control the bankruptcy risk at about 5% in the next five years. Parameter data reference and MCPRAM-algorithm can be used to design and develop new insurance products in a random environment, and provide valuable decision support for the scientific operation and management of insurance institutions.