A Fourier-Cosine Method for Finite-Time Ruin Probabilities

38 Pages Posted: 30 Apr 2021

See all articles by Wing Yan Lee

Wing Yan Lee

The Hang Seng University of Hong Kong - Department of Mathematics and Statistics

Xiaolong Li

Southern University of Science and Technology

Fangda Liu

Georgia State University; University of Waterloo - Department of Statistics and Actuarial Science

Yifan Shi

Southern University of Science and Technology

S. C. P. Yam

The Chinese University of Hong Kong. Department of Statistics

Date Written: April 15, 2021

Abstract

In this paper, we study the finite-time ruin probability in the risk model driven by a L´evy 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 L´evy 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 Lt. 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.

Suggested Citation

Lee, Wing Yan and Li, Xiaolong and Liu, Fangda and Liu, Fangda and Shi, Yifan and Yam, Phillip, A Fourier-Cosine Method for Finite-Time Ruin Probabilities (April 15, 2021). Insurance: Mathematics and Economics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3832764

Wing Yan Lee

The Hang Seng University of Hong Kong - Department of Mathematics and Statistics ( email )

Hang Shin Link
Siu Lek Yuen
Shatin, Hong Kong
China

Xiaolong Li

Southern University of Science and Technology ( email )

1088 Xueyuan Avenue
Shenzhen, Guangdong 518055
China

Fangda Liu (Contact Author)

Georgia State University ( email )

35 Broad St NW
Apt 1110
Atlanta, GA 30303
United States
4703789998 (Phone)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Yifan Shi

Southern University of Science and Technology ( email )

1088 Xueyuan Avenue
Shenzhen, Guangdong 518055
China

Phillip Yam

The Chinese University of Hong Kong. Department of Statistics ( email )

Hong Kong

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