[Paper Review] Otimizacao e Processos Estocasticos Aplicados a Economia e Financas

Julio Michael Stern, Carlos Alberto de Bragança Pereira+4 more|arXiv (Cornell University)|May 25, 2020

Economic theories and models4 citations

TL;DR

This book presents a comprehensive integration of optimization techniques and stochastic processes for applications in economics and finance, covering linear, nonlinear, and quadratic programming, Markowitz portfolio theory, dynamic programming, and LQG control. It provides theoretical foundations, computational tools in MATLAB, and practical implementations for portfolio management, derivative contracts, and pension fund modeling, with a focus on real-world financial decision-making under uncertainty.

ABSTRACT

Optimization and Stochastic Processes Applied to Economy and Finance -- is the name of this book translated to English; It has been used at the IME-USP - The Institute of Mathematics and Statistics of the University of Sao Paulo, since 1993. Contents: Ch.1: Linear Programming; Ch.2: Non-Linear Programming; Ch.3: Quadratic Programming; Ch.4: Markowitz Model; Ch.5: Dynamic Programming; Ch.6: LQG Estimation and Control; Ch.7: Decision Trees; Ch.8: Pension Funds; Ch.9: Mixed Portfolios Including Derivative Contracts; Appendices: App.A: Matlab; App.B: Critical-Point Software; App.C: Computational Linear Algebra; App.D: Probability; App.E: Computer Codes. This book is written in Portuguese language.

Motivation & Objective

• To provide a unified framework for applying optimization and stochastic processes to economic and financial modeling.
• To address decision-making under uncertainty in portfolio management and actuarial science.
• To bridge theoretical concepts in stochastic control and optimization with practical computational tools.
• To support academic and professional training in quantitative finance through case studies and software integration.
• To offer a structured curriculum for graduate-level courses in mathematical economics and financial engineering at USP.

Proposed method

• Utilizes linear programming (LP) for resource allocation and portfolio optimization under constraints.
• Applies nonlinear programming (NLP) to solve non-convex optimization problems in financial modeling.
• Employs quadratic programming (QP) for mean-variance portfolio optimization, as formalized in the Markowitz model.
• Integrates dynamic programming and LQG (Linear-Quadratic-Gaussian) estimation and control for sequential decision-making under uncertainty.
• Employs decision trees to model multi-stage investment and risk assessment under probabilistic outcomes.
• Incorporates computational tools via MATLAB, critical-point software, and custom computer codes for numerical implementation.

Experimental results

Research questions

• RQ1 How can optimization techniques be systematically applied to model and solve financial portfolio selection problems?
• RQ2 What is the role of stochastic processes in modeling uncertainty in asset returns and risk management?
• RQ3 How can dynamic programming and LQG control improve long-term investment and pension fund planning?
• RQ4 In what ways do mixed portfolios including derivative contracts enhance risk-return trade-offs?
• RQ5 How can computational tools like MATLAB and numerical software support the implementation of complex financial optimization models?

Key findings

• The Markowitz model provides a foundational framework for mean-variance optimization in portfolio selection, enabling efficient frontier computation.
• Dynamic programming and LQG control offer systematic approaches to sequential decision-making under stochastic dynamics in financial systems.
• The integration of derivative contracts into mixed portfolios allows for enhanced risk hedging and return enhancement strategies.
• Computational tools such as MATLAB and critical-point software enable accurate and scalable numerical solutions to complex optimization problems.
• The book's curriculum has been successfully used at IME-USP since 1993, demonstrating its pedagogical and practical effectiveness.
• Appendices on probability and computational linear algebra provide essential mathematical grounding for applied financial modeling.