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Q: Certainty Equivalence in stochastic dynammic programming (\$50) ( No Answer,   0 Comments ) Question
 Subject: Certainty Equivalence in stochastic dynammic programming (\$50) Category: Science > Math Asked by: raidan-ga List Price: \$50.00 Posted: 24 Jul 2006 21:07 PDT Expires: 24 Jul 2006 21:54 PDT Question ID: 749215
 ```The notion of certainty equivalence in stochastic dynammic programming holds for linear quadratic utility functions. Does it also hold when the cost function has linear constraints on the decision space? For example, given the utility function U(t) = (x(t)+y(t)) * e(t) - M*(y(t))^2 x(t+1) = x(t) + y(t) U is the utility gained in period t, we choose y(t) to maxmize expected cumulative utility over say T periods. And M is a constant. e(t) is a random variable, for example it may be a mean reverting process (e(t) = b * e(t-1) + i(t), where b is a constant between zero and one, and i(t) is a random white noise term). In the above problem, if e(t) is a random variable then since the utility function is a quadratic, we can invoke certainty equivalence and just deal with the mean of e(t). However, if there are linear constraints on y(t), say y must be less than k, where k is some constant, does certainty equivalence still hold? If it does, are there any assumptions on the process generating e(t) that need to be made in order for certainty equivalence to hold?``` Clarification of Question by raidan-ga on 24 Jul 2006 21:40 PDT `When I mean linear constraints, I mean linear inequality constraints`   