A Monte Carlo Simulation Approach to Solve Two-Stage Stochastic Programming and Its Application to Bond Portfolio Optimization

Abstract

We present a Monte Carlo simulation-based approach for solving a stochastic twostage bond portfolio optimization problem, where the main objective is to minimize the total cost of the bond portfolio while making strategic decisions on bond purchases, holdings, and sales under uncertain market conditions such as interest rate fluctuations and future liabilities. The proposed algorithm not only identifies the appropriate number of randomly generated scenarios required to transform the stochastic problem into a deterministic one but also includes a stopping criterion to terminate the scenario generation process once further samples yield no significant improvement in the optimal solution. Additionally, we formulate a comprehensive two-stage model that allows the investor to make a buying, holding, or selling decision in both of the first and second stages, capturing the dynamic nature of investment strategy over time. The practical relevance of the methodology is demonstrated through its application to a real-world bond market dataset. The numerical results show that the proposed approach effectively minimizes costs, satisfies liability constraints, and provides a robust and flexible solution for bond portfolio optimization