Seminar by Marcos Escobar-Anel

Portfolio Optimization. A window into interesting problems and new developments

The proper investment of capital is one of the most consequential decisions for any financial company. There are many ingredients contributing to the complexity of this decision: an increase in stochastic factors driving market prices, the subsequent boost in parameter uncertainty, a strengthening of international and local regulations, the development of exotic customized products, just to mention a few. This presentation describes some of these challenges starting with basic models and existing theories. We use a combination of mathematical and financial concepts, including but not limited to expected utility theory, stochastic volatility processes, and optimal control. Closed-form solutions to some of these problems are presented with an emphasis on their financial implications and benefits, some open problems and promising new approaches are briefly motivated.