Alocação ótima em ativos financeiros para formação de um plano de previdência

Abstract

The decisions concerning resource allocation in a portfolio of assets continue to generate a relevant amount of research. One example of such problems is the formation of a portfolio for pension fund. Pension plans with defined-contribution are characterized by a constant allocation in the first periods of contract, followed by a conservative non{constant allocation in the latter periods. This research offers a model of decision support which captures this change in the allocation behavior (myopic to {non-myopic) and is computationally efficient. The considered assets are stocks and governmental bonds. The problem is formulated via dynamic stochastic programming, complemented with Monte Carlo simulation to represent the multivariate behavior of asset rates of return. However, problems of this type are difficult to solve due to the dependence to scenario tree, in which the number of states grows exponentially with the number of stages. Characteristics of non-myopic utility functions are exploited to synthetize the initial periods in a single-period of decision. This approach allows the representation of the behavior change as well as, naturally, to reduce the required computational effort. To overcome the dependence of scenario tree, it is proposed an approximation of the optimal cost function in the later periods through a parametric model. With this approach, the need to construct a scenario tree is eliminated and a satisfactory solution may be obtained within limits computationally tractable. The obtained results show the adequacy of the proposed complementary approaches.