The Opportunity Process for Optimal Consumption and Investment with Power Utility

TL;DR

This paper introduces the opportunity process as a key tool for solving utility maximization problems in financial markets, providing insights into optimal strategies and consumption patterns.

Contribution

It presents the concept of the opportunity process for power utility maximization, linking it to optimal strategies, value functions, and dual problems in a semimartingale market.

Findings

Opportunity process characterizes optimal strategies and value functions.

Monotonicity properties of optimal consumption are established.

Framework applies to markets with and without intermediate consumption.

Abstract

We study the utility maximization problem for power utility random fields in a semimartingale financial market, with and without intermediate consumption. The notion of an opportunity process is introduced as a reduced form of the value process of the resulting stochastic control problem. We show how the opportunity process describes the key objects: optimal strategy, value function, and dual problem. The results are applied to obtain monotonicity properties of the optimal consumption.