The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 18, Number 6 (2008), 2421-2449.
Exit problem of a two-dimensional risk process from the quadrant: Exact and asymptotic results
Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem considered is that of the corresponding two-dimensional risk process first leaving the positive quadrant; another is that of entering the negative quadrant. When the claims arrive according to a Poisson process, we obtain a closed form expression for the ultimate ruin probability. In the general case, we analyze the asymptotics of the ruin probability when the initial reserves of both companies tend to infinity under a Cramér light-tail assumption on the claim size distribution.
Ann. Appl. Probab., Volume 18, Number 6 (2008), 2421-2449.
First available in Project Euclid: 26 November 2008
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Zentralblatt MATH identifier
Secondary: 60F10: Large deviations 60G50: Sums of independent random variables; random walks
Avram, Florin; Palmowski, Zbigniew; Pistorius, Martijn R. Exit problem of a two-dimensional risk process from the quadrant: Exact and asymptotic results. Ann. Appl. Probab. 18 (2008), no. 6, 2421--2449. doi:10.1214/08-AAP529. https://projecteuclid.org/euclid.aoap/1227708924