马氏转移高敏感跳扩散CKLS模型的解及金融应用

将马氏转移切换机制和泊松过程引入到CKLS短期利率模型中,构建马氏转移跳扩散CKLS模型.理论方面,利用Lyapunov函数方法证明了马氏转移跳扩散CKLS模型存在唯一的全局正解并给出了该解的分析性质(包括一阶矩二阶矩的有界性,随机有界性和路径估计);用欧拉离散化方法得到马氏转移跳扩散CKLS模型的欧拉数值解,证明了其依概率收敛于解析解.应用方面,以债券定价和障碍期权的期望收益为例给出了马氏转移跳扩散CKLS模型数值解的收敛性在金融领域中的应用.基于7天Shibor利率的实证分析,说明了马氏转移跳扩散CKLS模型对我国金融市场中动态利率建模更加合理和有效.     

Construction of continuous time Markovian arrival processes

Markovian arrival processes were introduced by Neuts in 1979 (Neuts 1979) and have been used extensively in the stochastic modeling of queueing, inventory, reliability, risk, and telecommunications systems. In this paper, we introduce a constructive approach to define continuous time Markovian arrival processes. The construction is based on Poisson processes, and is simple and intuitive. Such a construction makes it easy to interpret the parameters of Markovian arrival processes. The construction also makes it possible to establish rigorously basic equations, such as Kolmogorov differential equations, for Markovian arrival processes, using only elementary properties of exponential distributions and Poisson processes. In addition, the approach can be used to construct continuous time Markov chains with a finite number of states     

H_2/H_∞ Control for Stochastic Jump-Diffusion Systems with Markovian Switching

In this paper, a stochastic H_2/H_∞ control problem is investigated for Poisson jumpdiffusion systems with Markovian switching, which are driven by a Brownian motion and a Poisson random measure with the system parameters modulated by a continuous-time finite-state Markov chain.A stochastic jump bounded real lemma is proved, which reveals that the norm of the perturbation operator below a given threshold is equivalent to the existence of a global solution to a parameterized system of Riccati type differential equations. This result enables the authors to obtain sufficient and necessary conditions for the existence of H_2/H_∞ control in terms of two sets of interconnected systems of Riccati type differential equations.     

Four step scheme for general Markovian forward-backward SDES

<正> This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward generator requires only mild regularity assumptions.The authors showthat the Four Step Scheme introduced by Ma,et al.(1994) is still effective in this case.Namely,the authors show that the adapted solution of the FBSDE exists and is unique over any prescribedtime duration;and the backward components can be determined explicitly by the forward componentvia the classical solution to a system of parabolic integro-partial differential equations.An importantconsequence the authors would like to draw from this fact is that,contrary to the general belief,in aMarkovian set-up the martingale representation theorem is no longer the reason for the well-posednessof the FBSDE,but rather a consequence of the existence of the solution of the decoupling integralpartialdifferential equation.Finally,the authors briefly discuss the possibility of reducing the regularityrequirements of the coefficients by using a scheme proposed by F.Delarue (2002) to the current case.     

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES

In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.     

Distributed Nonsmooth Convex Optimization over Markovian Switching Random Networks with Two Step-Sizes

This paper investigates the distributed convex optimization problem over a multi-agent system with Markovian switching communication networks. The objective function is the sum of each agent's local nonsmooth objective function, which cannot be known by other agents. The communication network is assumed to switch over a set of weight-balanced directed graphs with a Markovian property. The authors propose a consensus sub-gradient algorithm with two time-scale step-sizes to handle the Markovian switching topologies and the absence of global gradient information. With proper selection of step-sizes, the authors prove the almost sure convergence of all agents' local estimates to the same optimal solution when the union graph of the Markovian network' states is strongly connected and the Markovian chain is irreducible. The convergence rate analysis is also given for specific cases.Simulations are given to demonstrate the results.     

Finite-time stability and stabilization of Markovian switching stochastic systems with impulsive effects

Many practical systems in physics,biology,engineering and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes.The problems of finite-time stability analysis are investigated for a class of Markovian switching stochastic systems,in which exist impulses at the switching instants.Multiple Lyapunov techniques are used to derive sufficient conditions for finite-time stochastic stability of the overall system.Furthermore,a state feedback controller,which stabilizes the closed loop systems in the finite-time sense,is then addressed.Moreover,the controller appears not only in the shift part but also in the diffusion part of the underlying stochastic subsystem.The results are reduced to feasibility problems involving linear matrix inequalities (LMIs).A numerical example is presented to illustrate the proposed methodology.     

短期降雨预测的随机微分模型

在Nakita等的确定型短期降雨预测模型的基础上，利用随机微分方程理论。给出了预测降雨强度的随机模型．通过随机分析理论，求出了随机模型的解，同时研究了求解的近似数值方法和利用Fourier变换转化该随机降雨模型方程为常微分方程组的可行性．最后把文章提出的随机波动模型和NAk．klta提出的确定型短期预测模型运用到Nakita 1996年给出的降雨事件中进行预测和比较，效果良好．     

Robust H_∞ Control for Uncertain Markovian Jump Linear Time-Delay Systems

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Pareto Efficiency of Finite Horizon Switched Linear Quadratic Differential Games

A switched linear quadratic (LQ) differential game over finite-horizon is investigated in this paper. The switching signal is regarded as a non-conventional player, afterwards the definition of Pareto efficiency is extended to dynamics switching situations to characterize the solutions of this multi-objective problem. Furthermore, the switched differential game is equivalently transformed into a family of parameterized single-objective optimal problems by introducing preference information and auxiliary variables. This transformation reduces the computing complexity such that the Pareto frontier of the switched LQ differential game can be constructed by dynamic programming. Finally, a numerical example is provided to illustrate the effectiveness.     

Research on robust mean square stability of networked control systems with packet dropout

This paper is concerned with the robust stabilization problem of networked control systems with stochastic packet dropouts and uncertain parameters. Considering the stochastic packet dropout occuring in two channels between the sensor and the controller, and between the controller and the actuator, networked control systems are modeled as the Markovian jump linear system with four operation modes. Based on this model, the necessary and sufficient conditions for the mean square stability of the deterministic...     

α可靠规划与α可靠解法──解随机规划问题

本文首先论述了一般随机规划的几个概念，即随机约束条件、随机可行域和随机可行解．进而在总结其共性的基础上提出α可靠规划与α可靠解的概念和一种求解一般随机规划新方法—α可靠解法．α可靠解反映了随机规划可行解的特点，使随机规划可行解有了新含义，这在理论上和实际上都非常必要．文中分别讨论了用新方法求解随机约束规划、随机目标函数规划和一般随机规划问题，均有求解实例．同时还叙述了几种情况下的α可靠规划的约束条件换成等价的确定约束条件的问题，并给出了等价转换的证明．     

不确定随机跳变时滞系统非脆弱H∞滤

针对一类具有马尔可夫跳变参数的It^o类型不确定随机时滞系统,讨论了该类系统的鲁棒非脆弱H_∞滤波问题。在被控对象及滤波器同时存在不确定性的情况下,闭环滤波误差系统渐近稳定,干扰抑制性能指标小于给定上界。通过构造一个Lyapunov Krasovskii泛函,应用It^o微分公式沿系统对其求微分,再运用线性矩阵不等式（linear matrix inequality, LMI）和It^o公式,给出了非脆弱滤波器存在的可解性条件。通过数值算例表明了该方法的有效性。     

PMCMC for Term Structure of Interest Rates under Markov Regime Switching and Jumps

A parameter estimation method, called PMCMC in this paper, is proposed to estimate a continuous-time model of the term structure of interests under Markov regime switching and jumps.There is a closed form solution to term structure of interest rates under Markov regime. However, the model is extended to be a CKLS model with non-closed form solutions which is a typical nonlinear and non-Gaussian state-space model(SSM) in the case of adding jumps. Although the difficulty of parameter estimation greatly prevents from researching models, we prove that the nonlinear and non-Gaussian state-space model has better performances in studying volatility. The method proposed in this paper will be implemented in simulation and empirical study for SHIBOR. Empirical results illustrate that the PMCMC algorithm has powerful advantages in tackling the models.     

不对称信息下供应链最优激励契约的设计

对供应商和零售商之间的委托代理关系进行了分析研究,并将其归结为一个随机二层规划问题,通过给出适当的条件,证明了其解的存在性,并给出了所有的解.通过对解的分析,得到了有意义的经济学结论.     

PRODUCTIVE GOVERNMENT EXPENDITURE IN A STOCHASTICALLY GROWING OPEN ECONOMY

This paper employs a stochastic endogenous growth model with productive government expenditure in a small open economy to analyze the optimal fiscal policy. First, a stochastic model of a small open economy is constructed. Second, the equilibrium solutions of the representative agent＇s stochastic optimization problem are derived. Third, we obtain the equilibrium solutions of the central planner＇s stochastic optimization problem and the optimal government expenditure policy. Finally, the optimal tax policy is characterized.     

Robust H∞ filtering for discrete-time systems with Markovian switching and time-delays

The robust H∞ filtering problem for uncertain discrete-time Markovian jump linear systems with modedependent time-delays is investigated. Attention is focused on designing a Markovian jump linear filter that ensures robust stochastic stability while achieving a prescribed H∞ performance level of the resulting filtering error system, for all admissible uncertainties. The key features of the approach include the introduction of a new type of stochastic Lyapunov functional and some free weighting matrix variables. Sufficient conditions for the solvability of this problem are obtained in terms of a set of linear matrix inequalities. Numerical examples are provided to demonstrate the reduced conservatism of the proposed approach.     

Valuation of stock loans under a Markov chain model

In recent years the use of Markov chain models to model stock price movement has received increased attention among researchers. Markov chain models combine the discrete movements of a binomial tree model while retaining the Markovian properties of Brownian motion, thus allowing the best properties of both of these models. In this paper, the authors consider a Markov chain model in which the underlying market is solely determined by a two-state Markov chain. Such a Markov chain model is strikingly simple and yet appears capable of capturing various market movements. By proper selection of parameters, the Markov chain model can produce sample paths that are very similar to or very distinct from a classical Brownian motion, as the authors demonstrate in this paper. This paper studies the stock loan valuation, or the value of a loan in which a risky share of stock is used as collateral, under such a model. Dynamic programming equations in terms of variational inequalities are used to capture the dynamics of the problem. These equations are solved in closed-form. Explicit optimal solutions are obtained. Numerical examples are also reported to illustrate the results.     

ON SUFFICIENT AND NECESSARY OF EXISTENCE FOR A CLASS OF SINGULAR OPTIMAL STOCHASTIC CONTROL

We study a class of discounted models of singular stochastic control. In this kind of models, not only the structure of cost function has been extended to some general type, but also the state can be represented as the solution of a class of stochastic differential equations with nonlinear drift and diffusion term. By the various methods of stochastic analysis, we derive the sufllcient and necessary conditions of the existence of optimal control.