本文選題：倒向隨機微分方程　切入點：比較定理　出處：《中國科學(xué)技術(shù)大學(xué)》2017年碩士論文

【摘要】：本文以 Shi[1]的"Backward Stochastic Differential Equations in Finance" 為基礎(chǔ),簡述倒向隨機微分方程(BSDE)相關(guān)基礎(chǔ)知識及應(yīng)用。Liang等人[2]在"Backward Stochastic Dynamics on a filtered probability Space" 中介紹了 BSDE可以重新表示為某一軌道空間上的一般微分方程,Shi將其思路應(yīng)用到如下類型的倒向隨機微分方程dYtj=-fj(t,Yt,L(M)t)dt + dMtj,YTj= ξj,其中L是將M映射到適應(yīng)過程L(M)的給定非線性映射,修正項M是需要確定的鞅。Liang等人給出了某些條件下L2解的存在唯一性,Shi將其推廣到Lp解并證明了這些條件下Lp解的存在唯一性。更進一步,Shi給出了這類倒向隨機微分方程關(guān)于L2解的比較定理。最后,基于Liang等人的文章,Shi研究了經(jīng)典BSDE dYt =-f(t,Yt,Zt)dt + Zt*dBt,YT = ξj,L2解的Malliavin導(dǎo)數(shù)�；诒疚囊延械慕Y(jié)論,重新回顧并證明了一些其他文獻中重要的定理。最后,簡要的介紹了本文結(jié)論在金融市場中的應(yīng)用,例如,收益為ξ≥0,到期日為T的歐式期權(quán)定價。并且應(yīng)用Malliavin導(dǎo)數(shù)研究了某些條件下的期權(quán)定價。
[Abstract]:This paper is based on "Backward Stochastic Differential Equations in Finance" by Shi [1]. In "Backward Stochastic Dynamics on a filtered probability Space", the author introduces that BSDE can be rerepresented as a general differential equation in an orbital space. A type of backward stochastic differential equation, dYtjn -fjnt, Ytn, YTJ = 尉 _ j, where L is a given nonlinear mapping of M to the adaptive process LJ _ (M), The modified term M is a martingale. Liang et al. We give the existence and uniqueness of L2 solution under some conditions. Shi generalizes it to LP solution and proves the existence and uniqueness of LP solution under these conditions. Furthermore, Shi gives this kind of backward random solution. Comparison Theorems for L2 Solutions of differential equations. Based on Liang et al.'s paper, we have studied the Malliavin derivative of the solution of the classical BSDE dYt (BSDE dYt) -ftn (Ytn) Ztnt t (ZtBtT) = 尉 JN L2. Based on the conclusions in this paper, we have reviewed and proved some important theorems in other literatures. Finally, some important theorems in this paper are reviewed and proved. This paper briefly introduces the application of this conclusion in the financial market, for example, the European option pricing with a return of 尉 鈮，

本文編號：1674128