基于傅里叶级数展开式的有效期权定价方法

A novel option pricing method based on Fourier-cosine series expansion was proposed by Fang and Oosterlee. Developing their idea, three new option pricing methods based on Fourier, Fourier-cosine and Fourier-sine series expansions are presented in this paper, which are more efficient when the option prices are calculated with many strike prices. A series of numerical experiments under different exp-L~vy models are also given to compare these new methods with the Fang and Oosterlee＇s method and other methods.     

关于拟线性混合型边界问题的概率表示

关于某些抛物型和椭圆型偏微分方程的混合边界问题的解被表示为一类联系于Ito正向反射边界随机微分方程的反向随机微分方程的解．     

A NOTE ON PROBABILISTIC INTERPRETATION FOR QUASILINEAR MIXED BOUNDARY PROBLEMS

I.Intr0ducti0nWekn0wthattheprobabilisticrepresentationofsolutionsofpartialdifferentia1equationswiththemixedboundaryconditi0nshasmanyimp0rtantapplicationsbothintheoryofpartialdifferentialequationsandinthat0fstochasticdifferentialequationswithreflectingboun…     

关于有信用风险的期权定价的鞅方法

本文考虑了一个关于具有对方风险的衍生物的金融模型\bd 应用公司价值模型, 本文讨论了关于具有对方破产风险的衍生物的欧式期权定价问题\bd 应用鞅方法, 在高斯分布等的假设下本文得到并证明一个关于该期权的显式Black-Scholes定价公式\bd 该公式推广了Ammann在[1]中的相应结果.     

关于带跳的反射扩散过程的随机最优控制问题

研究一类半空间上带泊松跳的反射扩散过程的随机最优控制问题·　得到关于这一控制问题的非线性Nisio半群 ,和联系这一半群的带Neumann边界条件的哈密顿·雅可比·贝尔曼方程·　讨论这一类方程的粘性解的存在唯一性等问题·　证明该控制问题中的价值函数是这一方程的一个粘性解·     

A NOTE ON STOCHASTIC OPTIMAL CONTROL OF REFLECTED DIFFUSIONS WITH JUMPS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔｏｃｈａｓｔｉｃｏｐｔｉｍａｌｃｏｎｔｒｏｌｐｒｏｂｌｅｍｓｏｆｒｅｆｌｅｃｔｅｄｄｉｆｆｕｓｉｏｎｐｒｏｃｅｓｓｅｓｈａｓｂｅｅｎｃｏｎｓｉｄｅｒｅｄｂｙｓｏｍｅｍａｔｈｅｍａｔｉｃｉａｎｓ,ｆｏｒｉｎｓｔａｎｃｅ ,Ｐ .Ｌ .Ｌｉｏｎｓｉｎ [1 ] ,ａｎｄＪ.Ｌ .ＭｅｎａｌｄｉａｎｄＭ .Ｒｏｂｉｎｉｎ[2 ] .Ｉｎｔｈｉｓｐａｐｅｒ,ｗｅｗｉｌｌｃｏｎｓｉｄｅｒａｓｔｏｃｈａｓｔｉｃｏｐｔｉｍａｌｃｏｎｔｒｏｌｐｒｏｂｌｅｍｏｆｒｅｆｌｅｃｔｅｄｄｉｆｆｕｓｉｏｎｓｗｉｔ…     

关于解线性系统的一个有效的贝叶斯迭代方法

This paper concerns with the statistical methods for solving general linear systems. After a brief review of Bayesian perspective for inverse problems,a new and efficient iterative method for general linear systems from a Bayesian perspective is proposed.The convergence of this iterative method is proved,and the corresponding error analysis is studied.Finally, numerical experiments are given to support the efficiency of this iterative method,and some conclusions are obtained.