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A generalized defective renewal equation for the surplus process perturbed by diffusion. (English) Zbl 1074.91563
The authors consider the surplus process $$V(t)= u+ ct- S(t)+\sigma W(t)$$, $$t\geq 0$$, where $$\sigma> 0$$, $$\{W(t): t\geq 0\}$$ is a standard Wiener process, that is independent of the compound Poisson process $$\{S(t): t\geq 0\}$$. The defective renewal equation for the expected discounted function of a penalty at the time of ruin is generalized and its asymptotic formula is proposed.

##### MSC:
 91B30 Risk theory, insurance (MSC2010) 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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