博士论文，校内网应该会有图书馆权限，cnki和ilib都有。谢谢。


论文标题:倒向随机微分方程和非线性期望在金融中的应用：风险度量，定价机制的估计以及期权定价
Applications of Backward Stochastic Differential Equation and Nonlinear Expectations: Risk Measure, Option Pricing and Estimation of Evaluation Mechanism
论文作者
论文导师 PENG Shi-ge,论文学位 博士,论文专业 Probability and Mathematical Statistics
论文单位 山东大学,点击次数 25,论文页数 144页File Size4925K
2006-04-29论文网 http://www.lw23.com/lunwen_336934857/
backward stochastic differential equation; nonlinear expectation; SPAN;risk measure; nonparametric estimation; option pricing
倒向随机微分方程(BSDE)的线性形式首先由Bismut(1973)在引入，1990年Pardoux & Peng(1990)研究了Lipschitz条件下非线性倒向随机微分方程解的存在唯一性定理。Duffie & Epstein(1992b)在研究随机微分效用过程中也独立地引进了一类倒向随机微分方程。倒向随机微分方程在随机控制、偏微分方程、数理金融、经济等领域都有着广泛的应用。 经典的期望是一个线性泛函，在线性期望和可加测度之间存在一一对应的关系。但是这种一一对应的关系在非线性情形下并不成立，一般地，给定一个非线性期望，我们仍然可以导出一个非可加概率测度，但是却存在无穷多的非线性期望满足这一关系。因此在非线性情况下，期望比非可加测度更具特征性。Choquet(1954)用非可加测度定义了容度和Choquet期望，Choquet期望在统计、经济、金融和物理中有很多应用，但是它的缺点是很难定义条件Choquet期望。Peng(1997)通过一类特殊的倒向随机微分方程引入了一种非线性期望：g-期望。用g-期望可以很容易定义条件期望。不过g-期望是一种拟线性期望，也就是说，并不能包含完全非线性的情形。Peng(2005b)引入了一般的时间相容完全非线性期望和非线性马氏链，Peng(2006a，b)则提出G-期望的概念和理论。 Artzner，Delbaen，Eber & Heath(1997，1999)引入相容风险度量，作为一个公理化的工具量化金融头寸的风险。同在1997年，Peng(1997)引入了g-期望的概念。F(o|¨)llmer& Schied(2002a，b，c)和Frittelli & Rosazza Gianin(2002，2004)分别独立地研究了一般概率空间上的凸风险度量。动态风险度量也同样被提出，例如Cvitani(?) & Karatzas(1999)和Wang(1999)。Rosazza Gianin(2003)由g-期望引入一类动态风险度量，Jiang(2005b)做了进一步的研究，提出并证明了g-期望是相容风险度量或者凸风险度量的充分必要条件。Peng(2005b，2006a，b)研究的G-期望，G-布朗运动和相关It(?)类型的随机微积分，可以应用于风险度量。 Peng(2004b，d，2005a)提出并研究了时间相容估价和g-估价的理论，证明了满足一定条件的时间相容估价是一个g-估价，也就是说，无论用什么模型或者机制进行估价，只要验证满足定理条件，那么这个估价背后其实都有一个BSDE，其生成函数g就是定价机制，解z是对冲策略。因此一个很有意义的反问题是：如果已知BSDE的
The linear Backward Stochastic Differential Equation (BSDE) was first introduced by Bismut (1973). Pardoux & Peng (1990) proved the existence and uniqueness theorem of the solution of nonlinear BSDE under Lipschitz condition. Duffie & Epstein (1992b) also proposed a type of BSDE independently to characterize the stochastic differential utility (SDU). From then on, BSDE is further studied and applied widely in stochastic control, partial differential equation (PDE), mathematical finance and economics.The traditional expectation is a linear functional. There is a 1-1 correspondence between the traditional linear expectations and additive probability measures, but this 1-1 correspondence fails in nonlinear situations. In general, given a nonlinear expectation, one can still derive a nonadditive probability measure, but there exist an infinite number of nonlinear expectations satisfying the same relation. Thus in nonlinear situations the notion of expectation is more characteristic than that of non additive measures.Choquet (1954) extended the probability measure to capacity, and obtained definition of Choquet expectation. Choquet expectations have been applied in statistics, economics, finance and physics. But it is difficult to define conditional Choquet expectation in term of Choquet expectations. Peng (1997) introduced a kind of nonlinear expectation: g-expectation via a particular backward stochastic differential equation. Using Peng"s g-expectation, it is easy to define conditional expectations. But g-expectation is a quasi linear expectation, i.e. the fully nonlinear situation can not be covered, Peng (2005b) proposed more general F_t consistent nonlinear expectations and nonlinear Markovian chains, Peng (2006a,b) proposed the notation and theory of G-expectation.Coherent risk measure was introduce by Artzner, Delbaen, Eber & Heath (1997, 1999), and it is an axiomatic tool able to quantify riskiness of financial positions. Convex risk measures were firstly studied by Heath (2000), later, in general probability