Ruin probabilities for the phase-type dual model perturbed by diffusion

Abstract

In risk theory, ruin probabilities and dividend strategies have drawn lots of attentions. The dual risk model assumes that the surplus process decreases at a constant rate over time and gains by means of random jumps at random times, which is in accordance with real-life scenes such as life insurance. The dual model is widely used in describing security portfolio, pension funds, profits of enterprises whose income-generating depends on inventions or found, etc. In this paper, we consider a phase-type dual model perturbed by diffusion, whose inter-claim times are continuously distributed in phase-type distribution. We derive integro-differential equations, boundary conditions for ruin probability and obtain an explicit expression of the ruin probability when the phase-type distribution degenerates into the generalized Erlang (n) distribution. Finally, we obtain the integro-differential equations for the expected discounted dividend function under dividend payment with a threshold strategy.

Keywords:

• Phase-type distribution
• diffusion
• ruin probability
• integro-differential equation
• expected discounted dividend function

Data availability

The data used in this work is simulated by generalized Erlang(2) with parameters $\{{\lambda }_1,{\lambda }_2,c\}$ setted, anyone can verify and replicate our work by simulation and setting parameter$\{\delta ,{\sigma }^2\}.$

Additional information

Funding

The work is supported by the National Key Research and Development Plan (No. 2016YFC0800104) and the National Science Foundation of China (No. 71771203, 11671374, 71631006).