Padé approximants for finite time ruin probabilities

Xuan, Tran Dong

doi:10.1016/j.cam.2014.09.009

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2018

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“…This model embraces a huge literature in mathematical area. Beekman and Bowers, De Vylder, Ramsay, Garcia, Avram et al, Tran, etc proposed many different methods to compute ultimate and finite‐time ruin probabilities of insurance companies.…”

Section: Introductionmentioning

confidence: 99%

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

Xuan

Tuan

Kirane

2018

Math Methods in App Sciences

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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

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Section: Introductionmentioning

confidence: 99%