非期望效用理论框架下的金融随机优化问题研究

项目名称： 非期望效用理论框架下的金融随机优化问题研究

项目编号： No.61304065

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 自动化技术、计算机技术

项目作者： 米辉

作者单位： 南京师范大学

项目金额： 25万元

中文摘要： 行为金融是现代金融理论的研究热点，作为主要成果的秩相依效用理论和前景理论更是引起广泛的关注，如何在这些非期望效用理论框架下建立符合实际的投资决策模型，给出具体的量化方案，指导人们的投资决策，给随机优化理论带来了新的挑战。本项目将在非期望效用理论框架下，利用分位数函数、王-转换等处理概率扭曲问题的技术以及处理非凸/非凹函数的最优化问题的方法，结合随机控制、非线性期望、风险度量和数理金融方面的理论成果，研究金融市场中的股票、期权投资组合选择和期权定价问题，系统探讨这些问题中涉及到的随机优化难题。主要内容包括：基于非期望效用理论的最优股票投资策略；考虑持有期权头寸的投资策略；期权的最优持有头寸以及利用无差异定价原理、风险分解的思想等等，在投资组合模型基础上建立非期望效用理论下的期权定价模型。本项目的研究不仅可以充实现有的数理金融理论，也将推动随机优化理论的发展。

中文关键词： 非期望效用；概率扭曲；损失厌恶；随机优化；

英文摘要： Behavioral finance is a hot research topic in modern finance, and the main achievements,the rank dependent utility theory and prospect theory,attract a great deal of attention. Under the framework of these non-expected utility theories, how to construct investment decision models realistically, how to derive the specific quantization scheme, and how to instruct people to make reasonable investment decisions, have brought new challenges to stochastic optimization theory. Under the framework of non-expected utility theory, this project studies stock and option portfolio selection, and option pricing, and the corresponding stochastic optimiziton problem by using quantile function formulation, Wang-transform and other techniques dealing with the probability distortion problems and the optimization problems for non-convex/non-concave functions, combined with stochastic control theory, nonlinear expectation theory, risk measure theory and mathematical finance theory. The main issues investigated are as follows: optimal strategies for stock investment based on non-expected theory, optimal investment strategies for holding option positions, optimal position for options, and the model of option pricing based on the portfolio selection models by using the indifference pricing principle and factorization of risk.The resear

英文关键词： non-expected utility；probability distortion；loss aversion；stochastic optimization；