Expected Utility Optimization - Calculus of Variations Approach
Optimization and Control
2007-08-01 v1 Numerical Analysis
Abstract
In this paper, I'll derive the Hamilton-Jacobi (HJ) equation for Merton's problem in Utility Optimization Theory using a Calculus of Variations (CoV) Approach. For stochastic control problems, Dynamic Programming (DP) has been used as a standard method. To the best of my knowledge, no one has used CoV for this problem. In addition, while the DP approach cannot guarantee that the optimum satisfies the HJ equation, the CoV approach does. Be aware that this is the first draft of this paper and many flaws might be introduced.
Keywords
Cite
@article{arxiv.0707.4488,
title = {Expected Utility Optimization - Calculus of Variations Approach},
author = {Khoa Tran},
journal= {arXiv preprint arXiv:0707.4488},
year = {2007}
}