广义对偶选择理论下的最优支付
Optimal Payoff under the Generalized Dual Theory of Choice
摘要：
本文研究了单期完全市场中偏好模型下的投资组合优化问题。这个偏好模型包括Yaari的选择和分位数最大化的对偶理论作为特例。我们刻画了最优解存在的条件，并在最优解存在的条件下导出了最优解的封闭形式。最优投资组合的回报是一种数字期权：当市场好的时候，它产生一个价内回报，否则就没有回报。当初始财富增加时，好的市场情景集保持不变，而这些情景中的回报增加。最后，我们扩展了我们的投资组合优化问题，通过施加一个依赖结构与给定的基准收益，并得出类似的结果。
英文摘要：
We consider portfolio optimization under a preference model in a single-period, complete market. This preference model includes Yaari's dual theory of choice and quantile maximization as special cases. We characterize when the optimal solution exists and derive the optimal solution in closed form when it exists. The payoff of the optimal portfolio is a digital option: it yields an in-the-money payoff when the market is good and zero payoff otherwise. When the initial wealth increases, the set of good market scenarios remains unchanged while the payoff in these scenarios increases. Finally, we extend our portfolio optimization problem by imposing a dependence structure with a given benchmark payoff and derive similar results.
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