Premium
Regularization and error estimate of infinite‐time ruin probabilities for Cramer‐Lundberg model
Author(s) -
Tran Dong Xuan,
Nguyen Huy Tuan,
Kirane Mokhtar
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4867
Subject(s) - mathematics , tikhonov regularization , laplace transform , hadamard transform , truncation (statistics) , first hitting time model , fourier transform , regularization (linguistics) , mathematical analysis , calculus (dental) , inverse problem , statistics , computer science , medicine , dentistry , artificial intelligence
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.