金融风险中的定价及其准则探索和大偏差

项目名称： 金融风险中的定价及其准则探索和大偏差

项目编号： No.11301461

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 严钧

作者单位： 扬州大学

项目金额： 22万元

中文摘要： 随着新的金融衍生品不断涌现，在理论上要求我们对这些新的金融衍生品进行研究，在此背景下，本课题一方面拟对几类新的风险过程进行研究，具体地，我们拟研究这几类风险过程的泛函形式的大偏差和中偏差原理、中心极限定理和重对数律等，并将这些极限理论结果运用到对破产概率的研究上，得到破产概率的各种形式的渐近行为，找出最有可能引起破产的轨道，以及得到破产概率的指数不等式等等，这些结果可以给保险公司以理论指导，指导他们规避风险；该课题还准备对几类新的金融衍生品所对应的价格过程进行研究，找出这些价格过程在相对熵、Hellinger距离等准则下的最优鞅测度的表达形式或者刻画，探求这些不同准则下得到的最优鞅测度之间的相互联系，这些最优鞅测度的优良性比较；另外，我们还考虑探索新的鞅测度的选择准则，为金融公司对金融衍生品的合理定价提供理论上的支持。

中文关键词： 熵风险度量；偏差估计；大偏差原理；指数鞅；定价

英文摘要： With the emerging new financial derivatives, in theory, we need to study these new financial derivatives, in this context, on one hand, this subject plans to study several new risk processes, specifically, we intend to study the functional large and moderate deviation principles, central limit theorems and laws of iterated logarithm of the risk processes, then we apply thess limit theories to the study of ruin probabilities, get various forms of asymptotic behaviors of the ruin probabilities, identify the path which causes to ruin most likely, and we also obtain the exponential inequalities of the ruin probabilities etc, these results can be used to give theoretical guidance to the insurance companies and advise them to avoid risks; on the other hand, this subject is also intended to study the price processes with respect to several new financial derivatives, we want to identify the forms of expression or characterize of the optimal martingale measures of the price processes under the criteria of the relative entropy, Hellinger distance and so on, explore the linkages between these different optimal martingale measures, and compare the advantages and disadvantages of them; in addition, we also consider exploring the new martingale measure selection criteria to provide theoretical support for the rational pr

英文关键词： entropic risk measure；deviation estimation；large deviation principle；exponential martingale；pricing