Paper
The Compound Poisson Risk Model Perturbed by Diffusion with a Hybrid Dividend Strategy
- Authors:
- Peng Li; Chuancun Yin; Ming Zhou
- Abstract
- In this paper, we considered the compound Poisson risk model perturbed by diffusion with a hybrid dividend strategy. Firstly, we used Dynkin's formula to derive the integral-differential equations and boundary conditions satisfied by the expected total discounted dividends until ruin. For example, we obtained the explicit expression for the expected total discounted dividends by applying the integral-differential equations and boundary conditions when claims are exponentially distributed. Then we derived integral-differential equations with boundary conditions for the moment-generating functions and th moments of total discounted dividends until ruin. Finally, the famous Gerber-Shiu function was discussed, and the closed-form expression for the Laplace transform of the ruin time was solved when claims were exponentially distributed.
- Keywords
- Brownian Motion; Hybrid Dividend Strategy; Dividends; Dynkin's Formula; Moment-Generating Function; Gerber-Shiu Function
- StartPage
- 8
- EndPage
- 20
- Doi