A Fourier-cosine method for finite-time ruin probabilities
| Autor: | Sheung Chi Phillip Yam, Wing Yan Lee, Fangda Liu, Yifan Shi, Xiaolong Li |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Economics and Econometrics 050208 finance Characteristic function (probability theory) Subordinator 05 social sciences Probability density function 01 natural sciences 010104 statistics & probability Rate of convergence Survival function Approximation error 0502 economics and business Applied mathematics Rearrangement inequality 0101 mathematics Statistics Probability and Uncertainty Sine and cosine transforms Mathematics |
| Zdroj: | Insurance: Mathematics and Economics. 99:256-267 |
| ISSN: | 0167-6687 |
| Popis: | In this paper, we study the finite-time ruin probability in the risk model driven by a Levy subordinator, by incorporating the popular Fourier-cosine method. Our interest is to propose a general approximation for any specified precision provided that the characteristic function of the Levy Process is known. To achieve this, we derive an explicit integral expression for the finite-time ruin probability, which is expressed in terms of the density function and the survival function of L t . Moreover, we apply the rearrangement inequality to further improve our approximations. In addition, with only mild and practically relevant assumptions, we prove that the approximation error can be made arbitrarily small (actually an algebraic convergence rate up to 3, which is the fastest possible approximant known upon all in the literature), and has a linear computation complexity in a number of terms of the Fourier-cosine expansion. The effectiveness of our results is demonstrated in various numerical studies; through these examples, the supreme power of the Fourier-cosine method is once demonstrated. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect