On a Dual Risk Model with Dependent Structure and Proportional Gains
Xinran Feng *
School of Mathematics, Liaoning Normal University, Dalian, China.
Zhenhua Bao
School of Mathematics, Liaoning Normal University, Dalian, China.
*Author to whom correspondence should be addressed.
Abstract
This paper investigates a class of dual risk models featuring a dependent structure and a proportional gain mechanism. It is assumed that a dependency exists between the inter-arrival times of gains and the sizes of the gains, and that the surplus increases proportionally upon each gain event. Using renewal arguments, integral equations for the ruin probability and the ruin time are established. Series expressions for the ruin probability and the Laplace transform of the ruin time are derived by means of the Laplace transform, and the existence and convergence of the iterative solutions are proved. Numerical analysis reveals the effects of the proportional gain coefficient, the arrival rate, and the dependence parameter on the ruin probability. The results indicate that a higher gain frequency and a stronger positive dependence significantly reduce the ruin risk.
Keywords: Dual risk model, proportional gains, dependent structure, Laplace transform, Gerber-Shiu function