Regularization and error estimate of infinite-time ruin probabilities for Cramer-Lundberg model. (English) Zbl 1415.91152
Summary: 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.
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 44A10 | Laplace transform |
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