Applied Mathematics Colloquium: Subas Acharya (JHU)

Title: Stochastic Optimization in Finance and Energy Markets

Abstract:
This talk covers stochastic optimization models in finance and energy market problems. The first part examines an optimal control problem derived from a real options investment, where the investment timing and amount are the controls to maximize expected profit. The corresponding deterministic problem involves a non-smooth obstacle; due to this non-smoothness, both weak and strong solutions are proposed, with the strong solution based on certain thresholds. An application to renewable energy market problems is included, featuring empirical analysis. In the second part, it considers a dynamic wealth management problem formulated using another optimization model to determine optimal consumption, portfolio allocation, and investment policies. This includes analytical solutions for the one-dimensional case and deep learning solutions for the high-dimensional case.