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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:

60J75 Jump processes (MSC2010)
91B28 Finance etc. (MSC2000)
91B24 Microeconomic theory (price theory and economic markets)
91B30 Risk theory, insurance (MSC2010)
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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.