Optimization Models in Finance

Optimization has been a fundamental topic throughout human history. In ancient times, classic geometric problems, such as maximizing the area of a rectangle inscribed in a circle, exemplified this discipline. Today, optimization plays a crucial role across various fields, including physics, economics, engineering, and finance, serving as a powerful tool for identifying the best solutions from a set of feasible options.

I am particularly passionate about this topic in the MQF program at Rutgers Business School, where I have the privilege of learning from Professor Andrzej Ruszczyński. He is renowned for his expertise in optimizing nonlinear stochastic systems and excels at breaking down complex concepts into simple, intuitive explanations. His detailed and constructive lectures make the subject even more engaging.

This topic will explore optimization models in finance, focusing on the following key areas:

Introduction

• Introduction to Optimization

Theoretical Foundations

• Convex Sets and Functions
• Linear Programming
• Duality in Linear Programming
• Nonlinear Programming
• Duality in Nonlinear Programming

Applications in Finance

• Mean-Variance Portfolio Optimization
• Value at Risk (VaR)
• AVaR and Coherent Risk Measures