On the Smoothness of Value Functions

Bruno Strulovici and Martin Szydlowski

MPRA Paper from University Library of Munich, Germany

Abstract: We prove that under standard Lipschitz and growth conditions, the value function of all optimal control problems for one-dimensional diffusions is twice continuously differentiable, as long as the control space is compact and the volatility is uniformly bounded below, away from zero. Under similar conditions, the value function of any optimal stopping problem is continuously differentiable. For the first problem, we provide sufficient conditions for the existence of an optimal control, which is also shown to be Markov. These conditions are based on the theory of monotone comparative statics.

Keywords: Super Contact; Smooth Pasting; HJB Equation; Optimal Control; Markov Control; Comparative Statics; Supermodularity; Single-Crossing; Interval Dominance Order (search for similar items in EconPapers)
JEL-codes: C61 (search for similar items in EconPapers)
Date: 2012-01-07, Revised 2012-01-31
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Related works:
Working Paper: On the Smoothness of Value Functions (2012)
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