Optimum Allocation and Risk Measure in an Asset Liability Management Model for a Pension Fund Via Multistage Stochastic Programming and Bootstrap

This paper proposes an Asset Liability Management (ALM) multistage stochastic programming model and a new method for measuring and controlling the equilibrium risk of a pension fund in the Brazilian context. According to the Society of Actuaries, ALM can be defined as an ongoing financial management process of formulating, implementing, monitoring, and revising strategies related to assets, future investments, and liabilities in an attempt to achieve an organization’s financial objectives, future cash flow needs, and capital requirements, given the risk tolerances and other constraints. This is an optimization problem based on a scenario tree structure called multistage stochastic programming model. A pension fund optimal portfolio is one of the most common ALM applications. The main financial objective of a pension fund is to ensure the benefit payments by investing money from contributions. To do this, the investment policy must assure two conditions: equilibrium and liquidity- long and short term solvency. Several articles in literature have proposed stochastic programming models for optimal investment allocation. However, in all those works, the equilibrium risk is measured at the end of the planning horizon by comparing the final wealth in each scenario to a fixed capital requirement obtained independently from the investment policy adopted, assuming a portfolio of one fixed income contract without risk. We propose a method for measuring and controlling the equilibrium risk that takes into account the fact that the pension fun