英文标题：
《A Polynomial Scheme of Asymptotic Expansion for Backward SDEs and Option
pricing》
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作者：
Masaaki Fujii
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最新提交年份：
2014
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英文摘要：
A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion method, the dynamics of variables given by the forward SDEs is treated exactly. Although it requires a special form of the quadratic covariation terms of the continuous part, it allows rather generic drift as well as jump components to exist. The resultant approximation is given by a polynomial function in terms of the unperturbed forward variables whose coefficients are uniquely specified by the solution of the recursive system of linear ODEs. Applications to a jump-extended Heston and lambda-SABR models for European contingent claims, as well as the utility-optimization problem in the presence of a terminal liability are discussed.
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中文摘要：
提出了一种新的后向随机微分方程（BSDE）的渐近展开格式。引入扰动参数只是为了在BSDE内标度正向随机变量。与标准的小扩散渐近展开法相比，前向SDE给出的变量动力学得到了精确的处理。虽然它需要连续部分的二次协变项的一种特殊形式，但它允许存在相当普遍的漂移和跳跃分量。由此得到的近似值由一个多项式函数给出，该函数表示未受干扰的前向变量，其系数由线性常微分方程递归系统的解唯一指定。讨论了跳跃扩展的Heston和lambda-SABR模型在欧洲未定权益中的应用，以及存在终端负债时的效用优化问题。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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