Optimal stopping problems for matrix-exponential jump-diffusion processes

• Main Author: 蔡明耀
• Other Authors: 許元春
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/59160692321465414169

博士 === 國立交通大學 === 應用數學系所 === 100 === In this dissertation, we consider the optimal stopping problems for a general class of reward functions under the matrix-exponential jump-diffusion processes. Given the reward function in this class, following the averaging problem approach(see, for example, Alili and Kyprianou [1], Kyprianou and Surya [16], Novikov and Shiryaev [22], and Surya [27] ), we give an explicit formula for solutions of the corresponding averaging problem. Based on this explicit formula, we obtain the optimal boundary and the value function for the American optimal stopping problems. Also, we consider the pricing problems of perpetual American compound options under the matrix-exponential jump-diffusion processes. Following Gapeev and Rodosthenous [12], the initial two-step optimal stopping problems are decomposed into sequences of one-step problems for the underlying jump-diffusion process. In the double-exponential jump-diffusion model, we obtain the explicit pricing formula for the perpetual American compound option pricing problems. By our approach, we also recover results obtained in Gapeev and Rodosthenous [12]