Abstract: We propose a new type of Lévy subordinators, namely the truncated Lévy subordinator, which is obtained by restricting the size of each jump. The truncated Lévy subordinator is defined through the Lévy measure with the limitation that the jump sizes do not exceed a certain truncation level. We study the path properties of truncated Lévy subordinator and develop exact simulation algorithm based on marked renewal process. In particular, we study several examples of truncated Lévy subordinators, such as the Dickman process, the truncated gamma process, the truncated stable process, in details. This type of Lévy processes has various applications in finance and insurance. For instance, we could use these processes to model aggregate claims distributions as individual claim sizes are often bounded from above, or model loss distribution of insurers with excess of loss reinsurances. We also discover that the value of truncated Lévy subordinator at time t is the value of a perpetuity with stochastic discounting. Besides, we observe that this type of processes has a duality relationship with the Parisian stopping time of diffusion processes. Our algorithms therefore provide alternative methods for pricing Parisian options and bonds.

Bio: Yan Qu is a current PhD candidate in the Department of Statistics, probability in finance and insurance group. Her thesis is devoted to simulation-based study on Lévy processes and Lévy related stochastic models. Her main research interests include applied probability, computational finance, stochastic modeling and simulation. Prior to commencing her studies, Yan completed her undergraduate degree in Mathematics at Imperial College London and then her master’s degree in financial mathematics at London School of Economics and Political Science.