A Note on the Hamilton–Jacobi–Bellman Equation

May 1, 2026

A concise technical introduction to the Hamilton–Jacobi–Bellman equation and its applications in continuous-time optimal control and portfolio optimisation. Covers the verification theorem, viscosity solutions, and the classical Merton portfolio problem.

Contents

  1. The Control Problem
  2. The HJB Equation
  3. Portfolio Optimisation Example
  4. Conclusion

Suitable for graduate students and practitioners with a background in stochastic calculus.