A decomposition of the ruin probability for the risk process perturbed by diffusion
نویسنده
چکیده
In this paper, we consider the ruin probabilities (caused by oscillation or by a claim) of the classical risk process perturbed by diffusion and the risk process with return on investments. We will prove their twice continuous differentiability and derive the integro-differential equations satisfied by them. We will present the explicit expressions for them when the claims are exponentially distributed. © 2001 Elsevier Science B.V. All rights reserved.
منابع مشابه
Ruin in the Perturbed Compound Poisson Risk Process under Interest Force
In this paper, we study ruin in a perturbed compound Poisson risk process under stochastic interest force and constant interest force. By using the technique of stochastic control, we show that the ruin probability in the perturbed risk model is always twice continuously differentiable provided that claim sizes have continuous density functions. In the perturbed risk model, ruin may be caused b...
متن کاملRuin probabilities and decompositions for general perturbed risk processes
We study a general perturbed risk process with cumulative claims modelled by a subordinator with finite expectation, and the perturbation being a spectrally negative Lévy process with zero expectation. We derive a Pollaczek-Hinchin type formula for the survival probability of that risk process, and give an interpretation of the formula based on the decomposition of the dual risk process at modi...
متن کاملOn the expected discounted penalty function for a perturbed risk process driven by a subordinator
The Expected Discounted Penalty Function (EDPF) was introduced in a series of now classical papers [Gerber, H.U., Shiu, E.S.W., 1997. The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. Insurance: Math. Econ. 21, 129–137; Gerber, H.U., Shiu, E.S.W., 1998a. On the time value of ruin. N. Am. Actuar. J. 2 (1), 48–78; Gerber, H.U., Shiu, E.S.W.,...
متن کاملAsymptotics for the infinite time ruin probability of a dependent risk model with a constant interest rate and dominatedly varying-tailed claim sizes
This paper mainly considers a nonstandard risk model with a constant interest rate, where both the claim sizes and the inter-arrival times follow some certain dependence structures. When the claim sizes are dominatedly varying-tailed, asymptotics for the infinite time ruin probability of the above dependent risk model have been given.
متن کاملSome distributions for classical risk process that is perturbed by diffusion
In this paper we discuss the classical risk process that is perturbed by diffusion. We prove some properties of the supremum distribution of the risk process before ruin when ruin occurs and the surplus distribution at the time of ruin. We present the simple and explicit expression for these distributions when the claims are exponentially distributed. ©2000 Published by Elsevier Science B.V. Al...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001