A Review of Static Optimization Techniques for Optimal set-Liability Management

Simone Sbaraglia

2019-01-01

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Abstract

Let us consider the problem of a portfolio manager who has to manage an initial investment A0 until a fixed maturity T > 0. The manager is free to choose how to invest the money among a number of available assets and can periodically modify the portfolio composition, but has to satisfy several constraints both of endogenous and exogenous nature. From the point of view of a portfolio manager, a tool that is able to compute the optimal investment strategy in several different market conditions is very valuable. Having such a tool allows for a deeper understanding of the underlying problem, provides the optimal investment strategy under certain hypotheses on the stochastic evolution of the asset prices, makes it possible to derive empirical estimations of the error that could be faced for each choice of the investment strategy, makes it possible to test the robustness of a given strategy to changes in the macroeconomic parameters and so on. In this article we shall review some of the more widely used global optimization algorithms that can be applied to determining the best investment strategy for managers and practitioners and shall outline the main difference between static and dynamic optimization techniques.