Introduction to Stochastic Optimal Control under Constraints in Finance
Abstract
Among the various subfields of Financial Mathematics, Stochastic Optimal Control under Constraints (SOCC) answers specifically to the question of portfolio optimization while accounting for the stochastic nature of the financial markets and the restrictions imposed on the portfolio management (by regulators, for example). This presentation aims to serve as an introduction to SOCC by blending its theoretical aspects with practical applications and numerical methods. In particular, we will look at (1) a motivating example from Life Insurance, (2) Dynamic Programming Principle as the core of SOCC, and (3) some applications of Deep Learning for numerical estimation of the optimal controls.