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- Title
Optimal Investment and Consumption Decisions under the Constant Elasticity of Variance Model.
- Authors
Hao Chang; Xi-min Rong; Hui Zhao; Chu-bing Zhang
- Abstract
We consider an investment and consumption problem under the constant elasticity of variance (CEV)model, which is an extension of the originalMerton's problem. In the proposed model, stock price dynamics is assumed to follow a CEVmodel and our goal is to maximize the expected discounted utility of consumption and terminal wealth. Firstly, we apply dynamic programming principle to obtain theHamilton-Jacobi-Bellman (HJB) equation for the value function. Secondly, we choose power utility and logarithmutility for our analysis and apply variable change technique to obtain the closed-formsolutions to the optimal investment and consumption strategies. Finally, we provide a numerical example to illustrate the effect of market parameters on the optimal investment and consumption strategies.
- Subjects
INVESTMENTS; CONSUMPTION (Economics); ELASTICITY; ANALYSIS of variance; HAMILTON-Jacobi-Bellman equation; LOGARITHMS; STOCK prices
- Publication
Mathematical Problems in Engineering, 2013, p1
- ISSN
1024-123X
- Publication type
Article
- DOI
10.1155/2013/974098