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A Calculus of Variations Approach to Stochastic Control

Published: September 1, 2025 | arXiv ID: 2509.01744v1

By: Matthew Lorig

BigTech Affiliations: University of Washington

Potential Business Impact:

Helps make the best money choices for the future.

Business Areas:
Risk Management Professional Services

We use classical tools from calculus of variations to formally derive necessary conditions for a Markov control to be optimal in a standard finite time horizon stochastic control problem. As an example, we solve the well-known Merton portfolio optimization problem.

Country of Origin
🇺🇸 United States

Page Count
5 pages

Category
Mathematics:
Optimization and Control