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On the discounted penalty at ruin in a jump-diffusion and the perpetual put option. (English) Zbl 0924.60075
The paper deals with a stochastic model of ruin theory which is obtained by adding a Wiener process to the right side term of the classical non-random model. The corresponding expected discounted value of a penalty at ruin satisfies a renewal equation, which is obtained via a probabilistic approach. Pricing perpetual put options is examined, and the new equations so obtained extend classical known results already established by Merton.

MSC:
60J75Jump processes
91B28Finance etc. (MSC2000)
91B24Price theory and market structure
91B30Risk theory, insurance
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References:
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