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??In this paper, we prove the existence and uniqueness of solutions for reflected backward stochastic differential equations driven by a Levy process, in which the reflecting barriers are just right continuous with left limits whose jumps are arbitrary. To derive the above results, the monotonic limit theorem of Backward SDE associated with Levy process is established.     

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Brownian motion and normal distribution have been widely used in Cox-Ingersoll-Ross interest rate framework to model the instantaneous interest rate dynamics. However, empirical studies have also shown that the return distribution of interest rate has a higher peak and two fatter tails than those of the normal distribution. Meanwhile, when the rare catastrophic shocks occur or the regime shifts in the economy and finance, the money market may have jumps. In this paper, we will consider a class of reflected Cox-Ingersoll-Ross interest rate models with noise. Furthermore, we shall continue to supply the Laplace transform of the stationary distribution about this reflected diffusion process with jumps.     

Votre Levy Rampe-T-IL?

The paper gives a necessary and sufficient criterion on theLévy measure that determines whether a Lévy processcreeps. (The author says that a Lévy process creeps ifit can continuously pass a fixed level.)     

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??We consider a Markov switching exponential Levy model in which the
underlying economy switches between a finite number of states. The switching is modeled by a
hidden Markov chain. We explore the link between options prices in Markov switching exponential
Levy models and the related partial integro-differential equations in the case of European
options.     

金融中的Levy模型及其仿真

近20年来,金融中Levy模型与蒙特卡洛仿真技术日益受到重视. 在连续时间过程的金融建模中带跳跃的Levy模型相比于连续轨道的布朗运动模型能很好地刻画市场的跳跃,更好地拟合金融数据的统计特征,更准确地对衍生品定价. 但是,相较于经典的Black-Scholes模型,用Levy模型对衍生品定价以及求解对冲策略的计算复杂度大大增加. 蒙特卡洛仿真成为Levy模型计算中最重要的方法之一. 首先详细地介绍了Levy模型引入的背景,并引出仿真方法在其中重要的应用价值. 最后,简要地给出了Levy过程仿真及其梯度估计的基本方法.     

A Nonstandard Levy-Khintchine Formula and Levy Processes

We use methods from nonstandard analysis to obtain a short and simple derivation of the Levy-Khintchine formula via an explicit construction of certain laws of the infinitesimal increments. Consequently, any arbitrary Levy process is representable as the standard part of a hyperfinite sum of infinitesimal increments.     

基于Levy飞行改进蝴蝶优化算法

蝴蝶优化算法是一种模仿蝴蝶觅食行为群智能优化算法,充分利用蝴蝶的嗅觉来确定食物源的位置上,但是该算法与其他智能算法一样,也存在一些缺点和不足如收敛速度和求解精度等方面的问题,蝴蝶优化算法原理主要主要模仿蝴蝶种群寻找食物,每只蝴蝶都散发出一定浓度的香气,每只蝴蝶都会感受到周围其它蝴蝶的味道,并朝着那些散发更多香味的蝴蝶移...     

两指标Levy过程的强极限定理

本文研究了两指标Ｌｅｖ过程增量平方和的强极限，获得了一些重要结果。     

Option Pricing for Time-Change Exponential Levy Model Under Memm

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

马尔可夫交换Levy过程的最小熵鞅测度

研究了由马尔可夫交换Levy过程的随机指数所驱动的风险资产的期权定价问题,即市场的利率、风险资产的波动率以及N个状态的补偿子都依赖于不可观的经济状态,而这些经济状态服从于一个连续时间的隐马氏链模型.一般地,由马尔可夫交换Levy过程的随机指数所描述的市场是不完备的,因此,鞅测度不是唯一的.通过采用状态转换Esscher变换来确定等价鞅测度,并且证明了所得到的定价测度就是最小熵鞅测度.     

时间变换稳定Levy过程幂变差的极限定理

研究时间变换α-稳定Levy过程已实现幂变差的极限行为. 证明了规范化之后的已实现幂变差一致依概率收敛的大数定律, 并给出了除幂次$\frac \alpha 2$之外其它各幂次已实现幂变差的中心极限定理.     

On Comparison Theorem and Solutions of BSDEs for Levy Processes

In this paper, we consider backward stochastic differential equations driven by a Levy process. A comparison theorem and an existence and uniqueness theorem of BSDEs with non-Lipschitz coefficients are obtained.     

Gel＇fand三元组上分式Levy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Levy过程的随机积分，本文给出分式Levy过程的新息表示公式，此公式可将Gel＇land三元组上分式Levy过程转换成更简单的Levy过程，并且可以应用在信号识别和行为金融学中．     

一类具有正跳的Levy过程的一个极值分布

本文利用风险分析中的破产概率与带正跳的levy过程的一类极值分布间的关系,求得了该极值分布的表达式.     

Reflected and Doubly Reflected BSDEs for Levy Processes： Solutions and Comparison

In this paper we study reflected and doubly reflected backward stochastic differential equations （BSDEs, for short） driven by Teugels martingales associated with L~vy process satisfying some moment condi- tions and by an independent Brownian motion. For BSDEs with one reflecting barrier, we obtain a comparison theorem using the Tanaka-Meyer formula. For BSDEs with two reflecting barriers, we first prove the existence and uniqueness of the solutions under the Mokobodski＇s condition by using the Snell envelope theory and then we obtain a comparison result.     

Levy分布参数估计的损失函数和风险函数的Bayes推断

给出了在共轭先验分布下,L evy分布参数估计的损失函数和风险函数的Bayes估计及其为保守估计的一般条件,说明了该条件的合理性,并用S&P 500$close数据进行了实证分析支持我们的结论.     

指数Levy跳扩散模型下一类新型期权的定价研究

在指数levy跳扩散模型下,通过在确定的两个时间点之间设置一个特定的常数障碍水平,构造出一类两时间点两资产最大或最小值障碍期权.这种新型期权具有两时间点彩虹期权与障碍期权的双重性质,使得该新型期权在未定权益定价方面的应用更为广泛.最后利用鞅方法,给出了该类期权的定价公式.     

Power Utility Maximization in an Exponential Levy Model Without a Risk-free Asset

We consider the problem of maximizing the expected power utility from terminal wealth in a market where logarithmic securities prices follow a Levy process. By Girsanov's theorem, we give explicit solutions for power utility of undiscounted terminal wealth in terms of the Levy-Khintchine triplet.     

On driftless one-dimensional SDE’s with respect to stable Levy processes

The time-dependent SDE dX _t = b(t, X _t−)dZ _t with X ₀ = x ₀ ∈ ℝ, and a symmetric α-stable process Z, 1 < α ⩽ 2, is considered. We study the existence of nonexploding solutions of the given equation through the existence of solutions of the equation in class of time change processes, where is a symmetric stable process of the same index α as Z. The approach is based on using the time change method, Krylov’s estimates for stable integrals, and properties of monotone convergence. The main existence result extends the results of Pragarauskas and Zanzotto (2000) for 1 < α < 2 and those of T. Senf (1993) for α = 2. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 4, pp. 517–531, October–December, 2007.