Facoltà di scienze economiche

A review of perturbative approaches for robust optimal portfolio problems

Trojani, Fabio ; Vanini, Paolo

In: Computational methods in decision-making, economics and finance, 2002, p. 109

Only a few intertemporal optimal consumption and portfolio problems in partial and general equilibrium can be solved explicitly. It is illustrated in the paper that perturbation theory is a powerful tool for deriving approximate analytical solutions for the desired optimal policies in problems where general state dynamics are admitted and a preference for robustness is present. Starting from the... More

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    Summary
    Only a few intertemporal optimal consumption and portfolio problems in partial and general equilibrium can be solved explicitly. It is illustrated in the paper that perturbation theory is a powerful tool for deriving approximate analytical solutions for the desired optimal policies in problems where general state dynamics are admitted and a preference for robustness is present. Starting from the perturbative approach proposed recently by Kogan and Uppal it is demonstrated how robust equilibria for some formulations of a preference for robustness in the literature can be solved. A crucial requirement for this approach is the existence of a known functional form for the candidate model solutions, a condition which is not satisfied by some models of a preference for robustness. For these cases, recent results by Trojani and Vanini can be used to obtain a perturbative solution to the Bellman equation of the relevant benchmark model and to give some formal conditions under which the perturbative solution converges to the correct one.