Chapter 12: Optimal Stochastic Control

The following sections are included:

• Optimal Stochastic Control: The Problem

• The Objective

• The Hamilton–Jacobi–Bellman (HJB) or Dynamic Programming Equation

• HJB Finite Horizon

• The Verification Theorem

• Infinite Time Horizon

• Solving the Optimal Stochastic Control Problem

• Problems in Economics

• Optimal Portfolio Rules

• Viscosity Solutions and Solvability of the HJB Equation

• The Deterministic Problem

• Classical and Weak Solutions

• The Stochastic Problem

• Reference