On consistency of optimal portfolio choice for state-dependent exponential utilities

TL;DR

This paper proves the existence and uniqueness of a consistent, market-adjusted risk aversion profile for state-dependent exponential utilities, ensuring optimal strategies remain consistent over time in arbitrage-free markets.

Contribution

It introduces a unique, market-consistent risk aversion process for state-dependent exponential utilities, extending the forward performance framework.

Findings

Existence of a unique risk aversion process ensuring strategy consistency.

Alignment with forward performance theory.

Identification of the optimal, market-adjusted risk profile.

Abstract

In an arbitrage-free simple market, we demonstrate that for a class of state-dependent exponential utilities, there exists a unique prediction of the random risk aversion that ensures the consistency of optimal strategies across any time horizon. Our solution aligns with the theory of forward performances, with the added distinction of identifying, among the infinite possible solutions, the one for which the profile remains optimal at all times for the market-adjusted system of preferences adopted.