A stochastic control model of investment,production, and consumption on a finite horizon |
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| Authors: | Xiaoru Han Fahuai Yi |
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| Affiliation: | 1. Department of Mathematics, Foshan University, Guangdong 528000, China;2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China |
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| Abstract: | In this paper, we consider a stochastic control problem on a finite time horizon. The unit price of capital obeys a logarithmic Brownian motion, and the income from production is also subject to the random Brownian fluctuations. The goal is to choose optimal investment and consumption policies to maximize the finite horizon expected discounted hyperbolic absolute risk aversion utility of consumption. A dynamic programming principle is used to derive a time‐dependent Hamilton–Jacobi–Bellman equation. The Leray–Schauder fixed point theorem is used to obtain existence of solution of the HJB equation. At last, we derive the optimal investment and consumption policies by the verification theorem. The main contribution in this paper is the use of PDE technique to the finite time problem for obtaining optimal polices. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | PDE technique dynamic programming principle optimal policies |
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