标题： 不完全市场中的投资组合优化以及由均值最大熵确定的价格约束 显示英文标题

标题： Portfolio optimization in incomplete markets and price constraints determined by maximum entropy in the mean

摘要： 一个投资组合优化问题的解总是受初始资本和可用市场资产价格的约束。 如果已知风险中性测度，那么每种资产的价格是该测度下资产价格的贴现期望值。 但如果市场是不完整的，风险中性测度不是唯一的，每种资产的价格有一个可能的范围，这可以与买卖价差相对应。 本文提出了一种有效的方法来确定不完整市场中一组资产的当前价格，并且这些价格符合投资组合优化问题的成本约束。 我们的主要方法是使用均值最大熵方法，从买卖市场数据调整一个扭曲函数。 这个扭曲函数起到风险中性测度的作用，用于对资产进行定价，它所确定的扭曲概率能够再现买卖市场价值。 我们进行了数值例子，以研究按照所提出的方法计算投资组合中资产价格对投资组合收益的影响。 显示英文摘要

摘要： A solution to a portfolio optimization problem is always conditioned by constraints on the initial capital and the price of the available market assets. If a risk neutral measure is known, then the price of each asset is the discounted expected value of the asset's price under this measure. But if the market is incomplete, the risk neutral measure is not unique, and there is a range of possible prices for each asset, which can be identified with bid-ask ranges. We present in this paper an effective method to determine the current prices of a collection of assets in incomplete markets, and such that these prices comply with the cost constraints for a portfolio optimization problem. Our workhorse is the method of maximum entropy in the mean to adjust a distortion function from bid-ask market data. This distortion function plays the role of a risk neutral measure, which is used to price the assets, and the distorted probability that it determines reproduces bid-ask market values. We carry out numerical examples to study the effect on portfolio returns of the computation of prices of the assets conforming the portfolio with the proposed methodology.