Department of Mathematics
The paper studies the joint distribution of the time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process that is perturbed by diffusion. We prove that the expected discounted penalty satisfies an integro-differential equation of renewal type, the solution of which can be expressed as a convolution formula. The asymptotic behaviour of the expected discounted penalty as the initial capital tends to infinity is discussed.
Deficit at ruin, Renewal equation, Time of ruin, Ruin probability, Surplus prior to ruin, Surplus process
Source Publication Title
Insurance: Mathematics and Economics
Copyright © 2003 Elsevier Science B.V. All rights reserved.
Research supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (project no. HKBU/2075/98P) and also by the National Natural Science Foundation of China (project no. 19801020).
Link to Publisher's Edition
Chiu, S. N., and C. C. Yin. "The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion." Insurance: Mathematics and Economics 33.1 (2003): 59-66.