Maximum principle for anticipated recursive stochastic optimal control problem with delay and Lvy processes

In this paper,we study the stochastic maximum principle for optimal control problem of anticipated forward-backward system with delay and Lvy processes as the random disturbance. This control system can be described by the anticipated forward-backward stochastic differential equations with delay and L′evy processes(AFBSDEDLs),we first obtain the existence and uniqueness theorem of adapted solutions for AFBSDEDLs; combining the AFBSDEDLs' preliminary result with certain classical convex variational techniques,the corresponding maximum principle is proved.     

An L 2-theory for a class of SPDEs driven by Lévy processes

In this paper we present an L 2-theory for a class of stochastic partial differential equations driven by Lévy processes.The coefficients of the equations are random functions depending on time and space variables,and no smoothness assumption of the coefficients is assumed.     

Generalized Backward Doubly Stochastic Differential Equations Driven by Lévy Processes with Continuous Coefficients

A new class of generalized backward doubly stochastic differential equations (GBDSDEs in short) driven by Teugels martingales associated with Lévy process are investigated. We establish a comparison theorem which allows us to derive an existence result of solutions under continuous and linear growth conditions.     

Successful couplings for a class of stochastic differential equations driven by Lvy processes

By constructing proper coupling operators for the integro-differential type Markov generator,we establish the existence of a successful coupling for a class of stochastic differential equations driven by L’evy processes.Our result implies a new Liouville theorem for space-time bounded harmonic functions with respect to the underlying Markov semigroups,and it is sharp for Ornstein-Uhlenbeck processes driven by α-stable L’evy processes.     

Uniform boundary Harnack principle for rotationally symmetric Lévy processes in general open sets

In this paper we prove the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous Lvy processes.     

Gel'fand三元组上分式Lévy过程的新息表示

借助于分式积分-微分算子和关于Gel'fand三元组上分式Lévy过程的随机积分,本文给出分式Lévy过程的新息表示公式,此公式可将Gel'fand三元组上分式Lévy过程转换成更简单的Lévy过程,并且可以应用在信号识别和行为金融学中.     

Stochastic Nonlinear Beam Equations with Lévy Jump

In this paper,we study stochastic nonlinear beam equations with Lévy jump,and use Lyapunov functions to prove existence of global mild solutions and asymptotic stability of the zero solution.     

Option Pricing for Time-Change Exponential Lévy Model Under Memm

The purpose of this article is to study the rational evaluation of European options price whenthe underlying price process is described by a time-change Lévy process.European option pricing formula isobtained under the minimal entropy martingale measure(MEMM)and applied to several examples of particulartime-change Lévy processes.It can be seen that the framework in this paper encompasses the Black-Scholesmodel and almost all of the models proposed in the subordinated market.     

A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H_2/H_∞ CONTROL WITH RANDOM JUMPS

A necessary maximum principle is given for nonzero-sum stochastic differential games with random jumps.The result is applied to solve the H_2/H_∞ control problem of stochastic systems with random jumps.A necessary and sufficient condition for the existence of a unique solution to the H_2/H_∞ control problem is derived.The resulting solution is given by the solution of an uncontrolled forward backward stochastic differential equation with random jumps.     

Heavy tails of a Lévy process and its maximum over a random time interval

Let {Xt,t0} be a Lévy process with Lévy measure ν on(∞,∞),and let τ be a nonnegative random variable independent of {Xt,t0}.We are interested in the tail probabilities of X τ and X(τ) = sup0≤t≤τXt.For various cases,under the assumption that either the Lévy measure ν or the random variable τ has a heavy right tail we prove that both Pr(X τ > x) and Pr(X(τ) > x) are asymptotic to Eτν((x,∞)) + Pr(τ > x/(0 ∨ EX 1)) as x →∞,where Pr(τ > x/0) = 0 by convention.     

Gel’fand三元组上由同一Lévy过程定义的不同分数Lévy过程之间的积分变换公式(英文)

本文利用Riemann-Liouville分数积分算子的半群性质以及分数Lévy过程的Wie-ner积分,给出由同一平方可积Lévy过程定义的不同分数Lévy过程之间的积分变换公式.     

Parameter Estimation for the Discretely Observed Vasicek Model with Small Fractional Lévy Noise

The statistical inference of the Vasicek model driven by small Levy process has a long history.In this paper,we consider the problem of parameter estimation for Vasicek model dX_t=(μ-θX_t)dt+εdL_t^d,t∈[0,1],X_0=x_0,driven by small fractional Lévy noise with the known parameter d less than one half,based on discrete high-frequency observations at regularly spaced time points{t_i=i/n,i=1,2,...,n}.For the general case and the null recurrent case,the consistency as well as the asymptotic behavior of least squares estimation of unknown parametersμandθhave been established as small dispersion coefficientε→0 and large sample size n→∞simultaneously.     

Smooth-pasting property on reflected Lévy processes and its applications in credit risk modeling

We study the smooth-pasting property for a class of conditional expectations with reflected Lévy process as underlying state process.A relationship between local times and regulators for the doubly reflected Lévy process is established.As applications,we derive the analytic pricing formula for a zero-coupon defaultable bond when the default intensity(resp.the stochastic loss rate)is modeled as one-sided(resp.double-sided)reflected Lévy processes.Finally,some numerical illustrations are provided.     

A geometric interpretation of the transition density of a symmetric Lévy process

We study for a class of symmetric Lévy processes with state space R n the transition density pt（x） in terms of two one-parameter families of metrics, （dt）t>0 and （δt）t>0. The first family of metrics describes the diagonal term pt（0）; it is induced by the characteristic exponent ψ of the Lévy process by dt（x, y） = ^1/2tψ（x-y）. The second and new family of metrics δt relates to ^1/2tψ through the formulawhere F denotes the Fourier transform. Thus we obtain the following "Gaussian" representation of the transition density: pt（x） = pt（0）e- δ2t （x,0） where pt（0） corresponds to a volume term related to tψ and where an "exponential" decay is governed by δ2t . This gives a complete and new geometric, intrinsic interpretation of pt（x）.     

Poisson Stable Solutions for Stochastic Differential Equations with Lévy Noise

In this paper,we use a unified framework to study Poisson stable(including stationary,periodic,quasi-periodic,almost periodic,almost automorphic,Birkhoff recurrent,almost recurrent in the sense of Bebutov,Levitan almost periodic,pseudo-periodic,pseudo-recurrent and Poisson stable)solutions for semilinear stochastic differential equations driven by infinite dimensional L′evy noise with large jumps.Under suitable conditions on drift,diffusion and jump coefficients,we prove that there exist solutions which inherit the Poisson stability of coefficients.Further we show that these solutions are globally asymptotically stable in square-mean sense.Finally,we illustrate our theoretical results by several examples.     

Dupire It\^{o}’s formula for the exponential synchronization of stochastic semi-Markov jump systems with mixed delay under impulsive control

This paper emphasizes the exponential synchronization for a class of stochastic semi-Markov jump systems with mixed delay via stochastic hybrid impulsive control. The impulsive sequence includes synchronous and asynchronous impulses with the impulsive gains being a sequence of stochastic variables. Inspired by the idea of average, a concept of ``average stochastic impulsive gain" is used to qualify the impulse intensity. Our approach expands Dupire functional It\^{o}$"s formula to the stochastic semi-Markov jump systems with mixed delay for the first time. Moreover, in view of the established Lyapunov functional, graph theory, and stochastic analysis theory, some exponential synchronization criteria for the systems are derived. The theoretical results are applied to a class of Chua"s circuit systems with semi-Markov jump and mixed delay. Some synchronization criteria for the circuit systems are provided. The simulation results verify the effectiveness of the theoretical results.     

A risky asset model based on Lévy processes and asymptotically self-similar activity time processes with long-range dependence

In the paper,using Lvy processes subordinated by‘asymptotically self-similar activity time’processes with long-range dependence,we set up new asset pricing models.Using the diferent construction for gamma(Γ)based‘asymptotically self-similar activity time’processes with long-range dependence from Finlay and Seneta(2006)we extend the constructions for inverse-gamma and gamma based‘asymptotically selfsimilar activity time’processes with integer-valued parameters and long-range dependence in Heyde and Leonenko(2005)and Finlay and Seneta(2006)to noninteger-valued parameters.