In this paper we consider the following interpretation of the formal definition
of time consistency: a policy is time consistent if and only if the
future planned decisions are actually going to be implemented. In particular
for risk averse multistage stochastic programming, we discuss a CVaR based
portfolio selection problem and compare a time consistent formulation to a
inconsistent one. For the latter, we discuss how different planned and implemented
decisions can be and develop a new way of measuring the impact
of a inconsistent policy on the objective function. In other words, we argue
that the first stage decision of a time inconsistent policy is sub-optimal and
we propose a methodology to compute the related sub-optimality gap. For
portfolio selection example, we present a sensitivity analysis by computing
this gap for different planning horizons and risk aversion levels. Finally, to motivate the use of the proposed time consistent formulation, we develop a
suitable economic interpretation for its recursive objective function based on
the certainty equivalent of the related preference function.
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