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Time consistency and risk averse dynamic decision models: Definition, interpretation and practical consequences

Birgit Rudloff (brudloff***at***princeton.edu)
Alexandre Street (street***at***ele.puc-rio.br)
Davi Valladão (davimichel***at***gmail.com)

Abstract: This paper aims at resolving a major obstacle to practical usage of time-consistent risk-averse decision models. The recursive objective function, generally used to ensure time consistency, is complex and has no clear/direct interpretation. Practitioners rather choose a simpler and more intuitive formulation, even though it may lead to a time inconsistent policy. Based on rigorous mathematical foundations, we impel practical usage of time consistent models as we provide practitioners with an intuitive economic interpretation for the referred recursive objective function. We also discourage time-inconsistent models by arguing that the associated policies are sub-optimal. We developed a new methodology to compute the sub-optimality gap associated with a time-inconsistent policy, providing practitioners with an objective method to quantify practical consequences of time inconsistency. Our results hold for a quite general class of problems and we choose, without loss of generality, a CVaR-based portfolio selection application to illustrate the developed concepts.

Keywords: Time Consistency, Dynamic Stochastic Programming, Risk Aversion, Conditional Value-at-Risk (CVaR), Portfolio Selection

Category 1: Stochastic Programming

Category 2: Applications -- OR and Management Sciences (Finance and Economics )

Citation: The final publication is available at The European Journal of Operational Research.


Entry Submitted: 12/06/2010
Entry Accepted: 01/14/2011
Entry Last Modified: 08/12/2014

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