Optimal Payoffs under State-dependent Preferences

TL;DR

This paper develops a new framework for portfolio optimization that incorporates investors' preferences dependent on economic states, allowing explicit characterization of optimal payoffs and extending classical utility models.

Contribution

It introduces a novel approach to account for state-dependent preferences in portfolio selection, providing explicit solutions and extending Merton's utility optimization.

Findings

Explicit characterization of optimal payoffs under state-dependent preferences

Extension of Merton's utility optimization to state-dependent cases

Applications in security design and stochastic target probability problems

Abstract

Most decision theories, including expected utility theory, rank dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which income is received. Optimal payoffs have their lowest outcomes when the economy is in a downturn, and this feature is often at odds with the needs of many investors. We introduce a framework for portfolio selection within which state-dependent preferences can be accommodated. Specifically, we assume that investors care about the distribution of final wealth and its interaction with some benchmark. In this context, we are able to characterize optimal payoffs in explicit form. Furthermore, we extend the classical expected utility optimization problem of Merton to the state-dependent situation. Some applications in security design are discussed in detail and we also solve some stochastic extensions of the target probability optimization problem.