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The first passage time problem for mixed-exponential jump processes with applications in insurance and finance

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Listed:
  • Chuancun Yin
  • Yuzhen Wen
  • Zhaojun Zong
  • Ying Shen

Abstract

This paper stidies 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.

Suggested Citation

  • Chuancun Yin & Yuzhen Wen & Zhaojun Zong & Ying Shen, 2013. "The first passage time problem for mixed-exponential jump processes with applications in insurance and finance," Papers 1302.6762, arXiv.org, revised Jun 2014.
    • Handle: RePEc:arx:papers:1302.6762
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    References listed on IDEAS

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    Cited by:

    1. Matija Vidmar, 2016. "Ruin under stochastic dependence between premium and claim arrivals," Papers 1602.04580, arXiv.org, revised Jun 2017.

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