The first passage time problem for mixed-exponential jump processes with applications in insurance and finance
AbstractThis 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1302.6762.
Date of creation: Feb 2013
Date of revision: Jun 2014
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