Optimal Payoff under the Generalized Dual Theory of Choice

TL;DR

This paper analyzes portfolio optimization under a generalized dual theory of choice, deriving conditions for optimal solutions and characterizing their digital payoff structure in a complete market setting.

Contribution

It introduces a unified framework for portfolio optimization under a broad class of preference models, including Yaari's dual theory, with explicit solutions and extensions.

Findings

Optimal payoff is a digital option in the market scenarios

Optimal payoff increases with initial wealth in good market states

Extension to dependence structures with benchmark payoffs

Abstract

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.