Diffusion approximations for a risk process with the possibility of borrowing and investment
- 1 January 1994
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics. Stochastic Models
- Vol. 10 (2) , 365-388
- https://doi.org/10.1080/15326349408807300
Abstract
A diffusion approximation is constructed for an insurance risk model which was considered by Embrechts and Schmidli [8], where the company is allowed to borrow money if needed and to invest money for large surpluses. Besides the weak convergence of a sequence of such processes to a diffusion, the convergence of the finite- and infinite-time ruin probabilities is shown. The ruin probabilities of the diffusion are calculated and, for two examples, compared with the exact values. The convergence of the corresponding infinite-time ruin probabilities for a diffusion approximation for the classical process is also shownKeywords
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