Valuation of Stock Loans Under a Markov Chain Model  

作　　者：PRAGER David ZHANG Qing 

机构地区：[1]Department of Mathematics,Anderson University [2]Department of Mathematics,The University of Georgia

出　　处：《Journal of Systems Science & Complexity》2016年第1期171-186,共16页系统科学与复杂性学报（英文版）

基　　金：supported in part by the Simons Foundation(235179 to ZHANG Qing)

摘　　要：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.

关 键 词：Closed-form solution Markov chain model stock loan 

分 类 号：O211.62[理学—概率论与数理统计]