Regularization and error estimate of infinite‐time ruin probabilities for Cramer‐Lundberg model

Abstract

MSC Classification: Primary 91B30; secondary 93A30, 46N30 In this article, we consider the problem of finding the ultimate ruin probability in the classical risk mode. Using Laplace transform inversion and Fourier transform, we obtain ultimate ruin probability of an insurance company. First, we show that this problem is ill-posed in the sense of Hadamard. Then, we apply the Tikhonov and truncation methods for establishing the approximate function for the ultimate ruin probability. Furthermore, convergence of the method, together with some examples, will be given. Finally, we present a numerical example to show efficiency of the method. KEYWORDSill-posed problem, Laplace transform inversion, ultimate ruin probabilities 3820