Utility maximization with habit formation of interaction

Abstract

In this paper, we analytically solve the utility maximization problem for a consumption set with multiple habit formation of interaction. Consumption is here composed of habitual and nonhabitual components, where habitual consumption represents the effect of past consumption. We further assume that the individual seeks to maximize his/her expected utility from nonhabitual consumption. Although there is usually no explicit solution of linear dynamic systems in the habit formation model, we study the functional minimum of habitual consumption. To solve the optimization problem with a general utility function, we adopt the convex dual martingale approach to construct the optimal consumption strategy and provide an economic interpretation for nearly every object throughout the solution process.