Abstract and Applied Analysis

The First Passage Time Problem for Mixed-Exponential Jump Processes with Applications in Insurance and Finance

Chuancun Yin, Yuzhen Wen, Zhaojun Zong, and Ying Shen

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Abstract

This paper studies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the first passage times and undershoot (overshoot) are obtained. As applications, we present explicit expression of the Gerber-Shiu functions for surplus processes with two-sided jumps, present the analytical solutions for popular path-dependent options such as lookback and barrier options in terms of Laplace transforms, and give a closed-form expression on the price of the zero-coupon bond under a structural credit risk model with jumps.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 571724, 9 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277093

Digital Object Identifier
doi:10.1155/2014/571724

Mathematical Reviews number (MathSciNet)
MR3232849

Zentralblatt MATH identifier
07022635

Citation

Yin, Chuancun; Wen, Yuzhen; Zong, Zhaojun; Shen, Ying. The First Passage Time Problem for Mixed-Exponential Jump Processes with Applications in Insurance and Finance. Abstr. Appl. Anal. 2014 (2014), Article ID 571724, 9 pages. doi:10.1155/2014/571724. https://projecteuclid.org/euclid.aaa/1412277093


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