摘要：In this paper, enlightened by the asymptotic expansion methodology developed by Li (2013) and Li and Chen (2016), we propose a Taylor-type approximation for the transition densities of the stochastic differential equations driven by the gamma processes, a special type of Lévy processes. After representing the transition density as a conditional expectation of Dirac delta function acting on the solution of the related SDE, the key technical method for calculating the expectation of multiple stochastic integrals conditional on the gamma process is presented. To numerically test the efficiency of our method, we examine the pure jump Ornstein–Uhlenbeck model and its extensions to two jump-diffusion models. For each model, the maximum relative error between our approximated transition density and the benchmark density obtained by the inverse Fourier transform of the characteristic function is sufficiently small, which shows the efficiency of our approximated method. This talk is based on a joint work with Fan Jiang and Jingping Yang.

报告人介绍: 臧鑫博士为kaiyun体育登录网页入口数学科学公司金融数学系访问助理教授，为本科生和研究生讲授《风险理论》和《金融数学与精算学专题选讲》等课程。主要研究方向为风险管理和应用随机过程，研究工作发表于《Quantitative Finance》、《Probability in the Engineering and Informational Sciences》等杂志。

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