导　　师： 何春雄

学科专业： 070103

授予学位： 硕士

作　　者： ;

机构地区： 华南理工大学

摘　　要： 当某项资产的支付流既依赖于基础资产的价格又可能受外界干预的影响时，资产的定价问题通常用状态转换模型来刻画．状态转换模型是对传统模型的调整，它可以用来刻画可能突发某些不确定因素的投资项目．在实际投资中，企业投资者往往会在资产价值达到某个心理预期值（阈值）时，选择终止合约或改变投资组合．因此要研究企业应该如何经营决策，如是否应该增加新投资或减少现有的投资，选择什么时机进行新项目、终止旧项目，甚至增减一台设备，都可以使用状态转换模型．根据转换策略的不同，状态转换问题可以分为单边干预的不可逆转换问题、双边干预的不可逆转换问题、可逆的转换问题等．而本文则研究单边干预的不可逆状态转换问题下的资产定价问题． 在研究资产定价问题时，资产价值往往用持有资产所获得的支付流的期望现值来计算．而要计算期望现值可以采用不同的方法，Francois Pascal,MorellecErwan/(2008/)/[17/]利用基础资产价格行为的强马氏性和停时的分布来实现期望现值的计算．而Boyarchenko Svetlana,Levendorskii Sergei/(2007/)/[2/]计算期望现值的方法另辟蹊径，他们在研究永久期权的资产定价问题时，利用基础资产价格行为过程的Lévy指数，通过期望现值算子的Wiener-Hopf分解来分步计算． Francois Pascal,Morellec Erwan/(2008/)/[17/]已经使用第一种方法得到了带状态转换的资产定价公式．而本文将Boyarchenko Svetlana,LevendorskiiSergei/(2007/)/[2/]研究永久期权的方法运用到状态转换问题中．分别根据上边不可逆干预和下边不可逆干预的不同转换策略，通过对期望现值算子进行Wiener-Hopf分解，给出了计算支付流的期望现值的具体步骤，得到状态转换问题中资产定价的一般计算方法．然后对具跌停和涨停的具体情形，得到了资产价格的闭形式表达式，并和第一种方法得到的结果作比较． When the profit stream of an asset depends on not only the price offundamental, but also the possible intervention expected from theauthority. The pricing problem is usually characterized by regime-switchmodel. Regime-switch problem is an adjust of traditional model; it isapplied to characterize the profit stream of an asset, which allowspossible unexpected events. In the actual investment, investors oftenchoose to terminate a contract or change a portfolio when the asset valuereach some psychological expectations /(threshold/). Thus,to study howshould an enterprise to operate or make decisions, such as adding a newinvestment or reduction of existing investment, choose the threadsholdfor new projects or terminate the old ones, even change a piece ofequipment, regime switch model can be used. According to differentstrategies, regime switch problem can be classified in one-sidedirreversible intervention, two-sided irreversible intervention,andstate-dependent switch policy ect. This paper is going to study thevalueation under one-sided irreversible intervention. In the study of asset pricing problems, asset price is usually calculatedby the expected present value of a stream. To calculate expected presentvalue, different methods can be used. Using strong Markov property of thefundemental and the distribution of stopping time, Francois Pascal,Morellec Erwan/(2008/)/[17/]gain a general formula. In the study of perpetualoptions, Boyarchenko Svetlana,Levendorskii Sergei/(2007/)/[2/]used Lévyexponent of the fundemental and Wiener-Hopf factorization of EPV operatorto calculate. Used the first method, Francois Pascal,Morellec Erwan/(2008/)/[17/]have gainedthe formular for asste pricing under regime switch problem. This paperwill apply the second method used in the study of perpetual options byBoyarchenko Svetlana,Levendorskii Sergei/(2007/)/[2/]to regime switchingproblems. According to the upper side and the lower side irreversibleintervention, using Wiener-Hopf factorization, the steps for calculatingthe expected present value of a stream is given, a formula for assetpricing under regime switch problem is gained. At last, we get the closedform expressions of limit situation and the lower limit situation, whichis compared with the result of the first method.

关 键 词： 布朗运动 状态转换 期望现值 分解

分 类 号： [F224 F233]

领　　域： [经济管理] [经济管理] [经济管理]