This paper deals with backward stochastic differential equations with jumps,whose data(the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonli...This paper deals with backward stochastic differential equations with jumps,whose data(the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonlinear path-dependent parabolic integrodifferential equations, and then obtains a new type of nonlinear Feynman-Kac formula related to such BSDEs with jumps under some regularity conditions.展开更多
This paper studies the first passage time problem for a reflected two-sided jump-diffusion risk model with the jumps having a hyper-Erlang distribution.The authors give the explicit closed-form expression for the join...This paper studies the first passage time problem for a reflected two-sided jump-diffusion risk model with the jumps having a hyper-Erlang distribution.The authors give the explicit closed-form expression for the joint Laplace transform of the first passage time and the overshoot for the reflected process.Finally,the formula is applied to the ruin problem under the barrier dividend strategy and the pricing of the Russian option.展开更多
This paper examines the term structure of interest rate empirically, and discovers that jump-diffusion process is better than pure diffusion process when describing the stochastic behavior of interest rate, which incl...This paper examines the term structure of interest rate empirically, and discovers that jump-diffusion process is better than pure diffusion process when describing the stochastic behavior of interest rate, which including jump risk. Using two-stage method to estimate the term structure of China government bond market. Fitting the initial term structure with B-spline approximation method, and then as input to jump-diffusion model parameter estimation. The result accounts for that term structure with jump can explain the actual conditions of China government bond market.展开更多
The problem of general exchange option pricing on jump-diffusion model is presented, we use the methods of the change of numeraire and martingale measure, and get the analytic solution of above option.
Consider a family of probability measures {vξ} on a bounded open region D C Rd with a smooth boundary and a positive parameter set {βξ}, all indexed by ξ∈δD. For any starting point inside D, we run a diffusion u...Consider a family of probability measures {vξ} on a bounded open region D C Rd with a smooth boundary and a positive parameter set {βξ}, all indexed by ξ∈δD. For any starting point inside D, we run a diffusion until it first exits D, at which time it stays at the exit point ξ for an independent exponential holding time with rate βξ and then leaves ξ by a jump into D according to the distribution ξ. Once the process jumps inside, it starts the diffusion afresh. The same evolution is repeated independently each time the process jumped into the domain. The resulting Markov process is called diffusion with holding and jumping boundary （DHJ）, which is not reversible due to the jumping. In this paper we provide a study of DHJ on its generator, stationary distribution and the speed of convergence.展开更多
基金supported by the National Natural Science Foundation of China(Nos.10921101,11471190)the Shandong Provincial Natural Science Foundation of China(No.ZR2014AM002)the Programme of Introducing Talents of Discipline to Universities of China(No.B12023)
文摘This paper deals with backward stochastic differential equations with jumps,whose data(the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonlinear path-dependent parabolic integrodifferential equations, and then obtains a new type of nonlinear Feynman-Kac formula related to such BSDEs with jumps under some regularity conditions.
基金supported by the Natural Science Foundation of China under Grant Nos.11301369,11401419the Natural Science Foundation of Jiangsu Province under Grant Nos.BK20130260,BK20140279
文摘This paper studies the first passage time problem for a reflected two-sided jump-diffusion risk model with the jumps having a hyper-Erlang distribution.The authors give the explicit closed-form expression for the joint Laplace transform of the first passage time and the overshoot for the reflected process.Finally,the formula is applied to the ruin problem under the barrier dividend strategy and the pricing of the Russian option.
文摘This paper examines the term structure of interest rate empirically, and discovers that jump-diffusion process is better than pure diffusion process when describing the stochastic behavior of interest rate, which including jump risk. Using two-stage method to estimate the term structure of China government bond market. Fitting the initial term structure with B-spline approximation method, and then as input to jump-diffusion model parameter estimation. The result accounts for that term structure with jump can explain the actual conditions of China government bond market.
文摘The problem of general exchange option pricing on jump-diffusion model is presented, we use the methods of the change of numeraire and martingale measure, and get the analytic solution of above option.
基金supported by National Natural Science Foundation of China(Grant No.11101433)the Fundamental Research Funds for the Central South University(Grant No.2011QNZT105)+1 种基金Doctorial Dissertation Program of Hunan Province(Grant No.YB2011B009)US National Science Foundation (Grant Nos.AMC-SS-0706713,DMS-0805929,NSFC-6398100 and CAS-2008DP173182)
文摘Consider a family of probability measures {vξ} on a bounded open region D C Rd with a smooth boundary and a positive parameter set {βξ}, all indexed by ξ∈δD. For any starting point inside D, we run a diffusion until it first exits D, at which time it stays at the exit point ξ for an independent exponential holding time with rate βξ and then leaves ξ by a jump into D according to the distribution ξ. Once the process jumps inside, it starts the diffusion afresh. The same evolution is repeated independently each time the process jumped into the domain. The resulting Markov process is called diffusion with holding and jumping boundary （DHJ）, which is not reversible due to the jumping. In this paper we provide a study of DHJ on its generator, stationary distribution and the speed of convergence.
