Combinatorial Optimization under Cardinality Constraints and Real Market Frictions on B3

Organization / Context: UFF / MESC
Timeline: 2026 - Present
Domain Category: Quantitative Finance
Technologies: Python, Gurobi, Pyomo, SciPy, R, LaTeX

Executive Overview

Professional master’s thesis formulating exact Mixed-Integer Quadratic Programming (MIQP) and Mixed-Integer Linear Programming (MILP) models with linearized Conditional Value-at-Risk (CVaR). Models dynamic allocation of statistical arbitrage equity portfolios on B3 with transaction costs, borrowing fees, and cardinality constraints.

Architecture & Data Flow

The diagram below illustrates the sanitized high-level component topology and data processing pipeline:

flowchart TD
  A[Dados de Ativos & Spreads B3] --> B[Estimador de Covariância & Retorno Esperado]
  B --> C[Mecanismo de Otimização MIQP / MILP]
  D[Restrições de Cardinalidade & Fricções Reais] --> C
  E[Linearização de CVaR & Controle de Drawdown] --> C
  C --> F[Resolvedor Matemático Gurobi / Pyomo]
  F --> G[Alocação Ótima de Portfólio de Arbitragem]

Key Engineering Highlights

• Applied Operations Research: Exact MIQP and MILP formulations tailored to high-dimensional quantitative asset allocation.
• Coherent Risk Management: Linearized Conditional Value-at-Risk (CVaR) minimization outperforming classical Markowitz variance.
• Real-World Market Frictions: Direct integration of brokerage fees, tax drag, slippage, and short-selling borrowing costs.