Optimal Investment Consumption Choices under Mispricing and Habit Formation

Ailing Shi, Jingyun Sun and Botao Liu ()
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Ailing Shi: School of Education, Lanzhou University of Arts and Science, Lanzhou 730010, China
Jingyun Sun: Center for Quantitative Analysis of Gansu Economic Development, Lanzhou University of Finance and Economics, Lanzhou 730020, China
Botao Liu: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730010, China

Mathematics, 2024, vol. 12, issue 14, 1-15

Abstract: This paper studies the optimal consumption and investment for an agent, considering statistical arbitrary opportunities caused by mispriced stocks. The agent exhibits consumption habit formation and has access to a risk-free asset, a market index, and a pair of mispriced stocks. The optimization problem is to find the optimal consumption and investment strategies to maximize the expected utility from consumption and terminal wealth. The utility of consumption stems from the difference between the consumption and habit levels. Based on the dynamic programming method, a verification theorem is provided, and the analytical solution of the optimization problem is obtained. The numerical results show the behaviors of our formulas and are used to make practical recommendations. By studying the sensitivity of consumption and investment strategies to habit formation, mispricing, and a delta-neutral arbitrage strategy, we uncover and analyze the behaviors of the agent. Meanwhile, we define and discuss the wealth-equivalent utility loss in three cases, including ignoring habit formation, ignoring mispricing, and adopting the delta-neutral arbitrage strategy.

Keywords: habit formation; mispricing; optimal strategies; utility loss; financial market (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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