Expected Utility Optimization - Calculus of Variations Approach

Details Expected Utility Optimization - Calculus of Variations Approach Expected Utility Optimization - Calculus of Variations Approach

2007-07-30

arxiv.org/abs/0707.4488v1

Mathematics

Optimization and Control

Scientific paper

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.

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