# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020029

## Utility maximization with habit formation of interaction

 1 Department of Actuarial Science, School of Insurance, , Central University of Finance and Economics Beijing 100081, China 2 Department of Actuarial Science, School of Insurance; , China Institute for Actuarial Science, , Central University of Finance and Economics, Beijing 100081, China

* Corresponding author: Yike Wang

Received  February 2019 Revised  September 2019 Published  February 2020

Fund Project: The first author is supported by Projects 11771466 and 11571388 supported by National Natural Science Foundation of China, and Program for Innovation Research in Central University of Finance and Economics

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.

Citation: Jingzhen Liu, Yike Wang, Ming Zhou. Utility maximization with habit formation of interaction. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020029
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