A Monte Carlo-Based Framework for Two-Stage Stochastic Programming: Application to Bond Portfolio Optimization

Area of Science:

• Quantitative Finance
• Operations Research
• Computational Finance

Background:

• Bond portfolio optimization is complex due to stochastic factors like interest rate fluctuations and liabilities.
• Existing methods may struggle with the dynamic and uncertain nature of bond markets.
• Efficiently managing bond portfolios requires robust decision-making under risk.

Purpose of the Study:

• To develop a Monte Carlo simulation-based approach for stochastic two-stage bond portfolio optimization.
• To optimize portfolio costs while managing bond purchases, holdings, and sales under random market conditions.
• To provide a practical and robust method for real-world bond market applications.

Main Methods:

• Utilizing Monte Carlo simulation to generate random market scenarios.
• Converting the stochastic optimization problem into a deterministic one.
• Solving the deterministic problem using Mixed-Integer Linear Programming (MILP).

Main Results:

• The proposed algorithm successfully determines the necessary number of scenarios for problem conversion.
• The method effectively minimizes bond portfolio costs.
• The approach ensures that liabilities are met under simulated market conditions.

Conclusions:

• The Monte Carlo simulation-based approach offers a viable solution for stochastic bond portfolio optimization.
• This method provides a robust framework for making optimal financial decisions in dynamic markets.
• The successful application to a real-world bond market demonstrates practical utility and effectiveness.