This article deals with the ruin probability in a Sparre Andersen risk process with the inter-claim times being Erlang distributed in the framework of piecewise deterministic Markov process （PDMP）. We construct an e...This article deals with the ruin probability in a Sparre Andersen risk process with the inter-claim times being Erlang distributed in the framework of piecewise deterministic Markov process （PDMP）. We construct an exponential martingale by virtue of the extended generator of the PDMP to change the measure. Some results are derived for the ruin probabilities, such as the general expressions for ruin probability, Lundberg bounds, CramerLundberg approximations, and finite-horizon ruin probability.展开更多
In this paper, we investigate a Sparre Andersen risk model perturbed by diffusion with phase-type inter-claim times. We mainly study the distribution of maximum surplus prior to ruin. A matrix form of integro-differen...In this paper, we investigate a Sparre Andersen risk model perturbed by diffusion with phase-type inter-claim times. We mainly study the distribution of maximum surplus prior to ruin. A matrix form of integro-differential equation for this quantity is derived, and its solution can be expressed as a linear combination of particular solutions of the corresponding homogeneous integro-differential equations. By using the divided differences technique and nonnegative real part roots of Lundberg＇s equation, the explicit Laplace transforms of particular solutions are obtained. Specially, we can deduce closed-form results as long as the individual claim size is rationally distributed. We also give a concise matrix expression for the expected discounted dividend payments under a barrier dividend strategy. Finally, we give some examples to present our main results.展开更多
文摘This article deals with the ruin probability in a Sparre Andersen risk process with the inter-claim times being Erlang distributed in the framework of piecewise deterministic Markov process （PDMP）. We construct an exponential martingale by virtue of the extended generator of the PDMP to change the measure. Some results are derived for the ruin probabilities, such as the general expressions for ruin probability, Lundberg bounds, CramerLundberg approximations, and finite-horizon ruin probability.
基金Supported by National Basic Research Program of China （973 Program） 2007CB814905, National Natural Science Foundation of China （Grant No. 10871102）, and the Keygrant Project of Chinese Ministry of Education （Grant No. 309009）
文摘In this paper, we investigate a Sparre Andersen risk model perturbed by diffusion with phase-type inter-claim times. We mainly study the distribution of maximum surplus prior to ruin. A matrix form of integro-differential equation for this quantity is derived, and its solution can be expressed as a linear combination of particular solutions of the corresponding homogeneous integro-differential equations. By using the divided differences technique and nonnegative real part roots of Lundberg＇s equation, the explicit Laplace transforms of particular solutions are obtained. Specially, we can deduce closed-form results as long as the individual claim size is rationally distributed. We also give a concise matrix expression for the expected discounted dividend payments under a barrier dividend strategy. Finally, we give some examples to present our main results.
