Motor Vehicle Insurance Anti-Fraud Modeling Based on a Stochastic Differential Game System

Abstract

In this paper, we regard policyholders, insurance companies, and government departments to be an anti-fraud supervision system, and we explore the supervision of motor vehicle insurance fraud from the perspective of a tripartite game. Taking into consideration the bad reputation records of policyholders as a state variable, through continuous accumulation in effective time, it creates a continuous growth-type warning effect on policyholders, and thus, effectively curbs policyholder fraud and false supervision by insurance companies. At the same time, by considering the influence of random factors on the anti-fraud game of motor vehicle insurance, in this paper, we establish a stochastic differential game model to explore the optimal strategy, the optimal income level, and the expectation and variance of the insured’s bad reputation record stock under the conditions of with and without government supervision. Finally, through a simulation analysis, it is found that the game with government supervision is more conducive to reduce the insured’s fraud intensity, and the simulation proves the impact of different parameters on system stability.