随机区间收益市场下的稳健效用优化研究

发布时间：2018-03-02 06:10

本文关键词： 加权期望效用悲观度无稳健套利风险中性概率测度参数二次规划　出处：《东华大学》2014年硕士论文　论文类型：学位论文

【摘要】：在随机区间收益市场下,风险资产的损益用随机区间表示,可以反映由于信息不完全与投资者主观认识等因素影响下的资产价值表现。论文在随机区间市场背景下讨论了期望效用优化问题,概率测度不确定情形下无稳健套利的稳定性以及效用优化问题。在随机区间收益市场下,以无稳健套利定价原则为基础,得到了与经典随机金融市场类似的风险中性概率测度。未定权益的价格可以由其未来收益和风险中性概率测度界定。当概率测度不确定时,产生了无稳健套利性质的稳定性问题。论文基于概率测度的全变差距离,给出了金融市场模型无稳健套利性质不随概率测度变化而改变的条件。论文基于加权期望效用模型讨论了投资者有初始消费和未来不确定财富情形下的效用优化问题。研究效用函数受未来不确定的随机状态和随机区间取值状态影响下的最优效用问题。给出了最优效用组合存在性的条件。并以最优效用组合为基础,构建了风险中性概率测度。同时也给出了最优加权期望效用的基本性质。论文最后讨论了资产未来损益的分布不确定情形下的效用优化问题。在此问题中,所获取的信息仅仅是基本证券未来损益表现的一阶矩和二阶矩,建立了稳健加权期望效用优化模型。通过适当方法将稳健目标转化为双重标准问题,并通过参数二次规划问题加以求解。
[Abstract]:In a stochastic interval income market, the gains and losses of risky assets are expressed in a random interval. It can reflect the performance of asset value under the influence of incomplete information and investors' subjective understanding. This paper discusses the expected utility optimization problem under the background of stochastic interval market. The stability and utility optimization problem of non-robust arbitrage under uncertain probabilistic measures. In the stochastic interval income market, based on the principle of no robust arbitrage pricing, A risk-neutral probability measure similar to the classical stochastic financial market is obtained. The price of contingent equity can be defined by its future income and risk-neutral probability measure. When the probabilistic measure is uncertain, Based on the total variation distance of probabilistic measure, the paper gives the condition that the property of no robust arbitrage in financial market model does not change with the change of probabilistic measure. Based on the weighted expected utility model, this paper discusses the utility optimization problem in the case of investors with initial consumption and uncertain wealth in the future. The utility function is studied by the future uncertain random state and random interval value state shadow. The conditions for the existence of optimal utility combination are given, and based on the optimal utility combination, The risk neutral probability measure is constructed, and the basic properties of optimal weighted expected utility are also given. Finally, the paper discusses the utility optimization problem in the case of uncertain distribution of future gains and losses of assets. In this problem, the information obtained is only the first and second moments of the future profit and loss performance of basic securities. A robust weighted expected utility optimization model is established. The robust objective is transformed into a double standard problem by appropriate methods and solved by the parametric quadratic programming problem.
【学位授予单位】：东华大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F830.91;F224

【参考文献】