A generalized defective renewal equation for the surplus process perturbed by diffusion. (Q1413299)

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.