On the variable two-step IMEX BDF method for parabolic integro-differential equations with nonsmooth initial data arising in finance

报告题目:On the variable two-step IMEX BDF method for parabolic integro-differential equations with nonsmooth initial data arising in finance 


邀请人:黄学海

报告人:王晚生 教授 上海师范大学

时间:2019年7月18日(周四)15:30-16:30

地点:红瓦楼723

摘要:The implicit-explicit (IMEX) two-step backward differentiation formula (BDF2) method with variable step-sizes, due to the non-smoothness of the initial data, is developed for solving parabolic partial integro-differential equation (PIDE), which describes the jump-diffusion option pricing model in finance. It is shown that the variable step-sizes IMEX BDF2 method is stable for abstract PIDE under suitable time step restrictions. Based on the time regularity analysis of abstract PIDE, the consistency error and the global error bounds for the variable step-sizes IMEX BDF2 method are provided. After time semi-discretization, spatial differential operators are treated by using finite difference methods and the jump integral is computed using the composite trapezoidal rule. A local mesh refinement strategy is also considered near the strike price because of the non-smoothness of the payoff function. Numerical results illustrate the effectiveness of the proposed method for European and American options under jump-diffusion models.