The ruin problem for a Wiener process with state-dependent jumps

Lefebvre, M.

doi:10.2478/jamsi-2020-0002

Abstract

Let X(t) be a jump-diffusion process whose continuous part is a Wiener process, and let T (x) be the first time it leaves the interval (0,b), where x = X(0). The jumps are negative and their sizes depend on the value of X(t). Moreover there can be a jump from X(t) to 0. We transform the integro-differential equation satisfied by the probability p(x) := P[X(T (x)) = 0] into an ordinary differential equation and we solve this equation explicitly in particular cases. We are also interested in the moment-generating function of T (x).

References

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The ruin problem for a Wiener process with state-dependent jumps

Abstract

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