TY - JOUR A2 - N’Guérékata, Gaston M. AU - Yin, Chuancun AU - Wen, Yuzhen AU - Zong, Zhaojun AU - Shen, Ying PY - 2014 DA - 2014/07/07 TI - The First Passage Time Problem for Mixed-Exponential Jump Processes with Applications in Insurance and Finance SP - 571724 VL - 2014 AB - 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. SN - 1085-3375 UR - https://doi.org/10.1155/2014/571724 DO - 10.1155/2014/571724 JF - Abstract and Applied Analysis PB - Hindawi Publishing Corporation KW - ER -