This paper proposes a multistage stochastic programming approach for the asset-liability management of Brazilian pension funds. We generate asset price scenarios with stochastic differential equations-Geometric Brownian Motion model for stocks and Cox-Ingersoll-Ross model for fixed income securities. Intertemporal solvency regulatory rules for Brazilian pension funds are considered endogenously in the model and enforced with a combinatorial constraint. A VaR probabilistic constraint is incorporated to obtain a positive funding ratio at each time period with high probability. Our approach uses multiple trees to provide a representative characterization of the uncertainty and is not computationally prohibitive. We evaluate the insolvency probability under different initial funding ratios through extensive simulations. The study reveals that the likely decrease of interest rate premiums in the next years will force pension fund managers to significantly change their portfolio strategies. They will have to take more risk in order to deliver the cash flows required to cover the liabilities and satisfy the regulatory constraints.
In this paper, we provide an empirical discussion of the differences among some scenario tree-generation approaches for stochastic programming. We consider the classical Monte Carlo sampling and Moment matching methods. Moreover, we test the Resampled average approximation, which is an adaptation of Monte Carlo sampling and Monte Carlo with naive allocation strategy as the benchmark. We test the empirical effects of each approach on the stability of the problem objective function and initial portfolio allocation, using a multistage stochastic chance-constrained asset-liability management (ALM) model as the application. The Moment matching and Resampled average approximation are more stable than the other two strategies.
We briefly discuss the differences among several methods to generate a scenario tree for stochastic optimization. First, the Monte Carlo Random sampling is presented, followed by the Fitting of the First Two Moments sampling, and lastly the Michaud sampling. Literature results are reviewed, taking into account distinctive features of each kind of methodology. According to the literature results, it is fundamental to consider the problem’s unique characteristics to make the more appropriate choice on sampling method.
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