CRRA Utility Maximization Over a Finite Horizon in an Exponential Levy Model with Finite Activity

Stefano Baccarin
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Stefano Baccarin: Department of Economics, Social Studies, Applied Mathematics and Statistics, University of Torino, Torino, Italy;

No 92, Working papers from Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino

Abstract: We study a dynamic portfolio optimization problem over a finite horizon with n risky securities and a risk-free asset. The prices of the risky securities are modelled by ordinary exponentials of jump- diffusions. The goal is to maximize the expected discounted utility from both consumption up to the final horizon and terminal wealth. We prove a verification theorem that characterize the value function and the optimal policy by means of a regular solution of a HJB partial integro-differential equation. The verification theorem is used to obtain closed-form expressions for the value function and the optimal policy considering power and logarithmic utility functions.

Keywords: Optimal consumption/investment over a finite horizon; CRRA utility; Dynamic programming; Levy processes with finite activity; Integro-differential PDE (search for similar items in EconPapers)
JEL-codes: D7 D72 H7 H70 H77 (search for similar items in EconPapers)
Pages: 25 pages
Date: 2024-04
New Economics Papers: this item is included in nep-upt
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