Decision Models for Liability Driven Investments: A Stochastic Approach

This thesis presents the implementation of a mathematical model aimed at optimizing a Liability-Driven Investment (LDI) portfolio that uses an immunization strategy through a stochastic approach. The model seeks to balance the portfolio's sensitivity to interest rate changes by aligning the PV01 (Price Value of a Basis Point) of the assets, consisting of government bonds, with the PV01 of the liabilities. The stochastic method introduces multiple scenarios of future interest rate trajectories, each with associated probabilities, enabling the optimization to consider uncertainty in financial markets. Additionally, a deterministic linear optimization model is developed for comparison, which assumes a single, fixed interest rate trajectory. Both models are evaluated on their effectiveness in achieving the desired liability matching under various conditions, with the results from the stochastic model providing a more robust solution in the presence of market instability. The comparison highlights the advantages and limitations of each approach in managing interest rate risk and achieving long-term liability matching objectives for an LDI portfolio.