A Dependent Insurance Risk Model with Surrender and Investment under the Thinning Process

A dependent insurance risk model with surrender and investment under the thinning process is discussed, where the arrival of the policies follows a compound Poisson-Geometric process, and the occurrences of the claim and surrender happen as the -thinning process and the -thinning process of the arrival process, respectively. By the martingale theory, the properties of the surplus process, adjustment coefficient equation, the upper bound of ruin probability, and explicit expression of ruin probability are obtained. Moreover, we also get the Laplace transformation, the expectation, and the variance of the time when the surplus reaches a given level for the first time. Finally, various trends of the upper bound of ruin probability and the expectation and the variance of the time when the surplus reaches a given level for the first time are simulated analytically along with changing the investment size, investment interest rates, claim rate, and surrender rate.