On the Smoothness of Value Functions

descriptionPublicationkeyboard_double_arrow_right Article , Research , Preprint , Report 01 Jan 2012 Germany English Publisher:Elsevier BVJournal:SSRN Electronic Journal (eissn: 1556-5068,

Copyright policy )Funded by:NSF | CAREER: Comparative Stati...

Authors: Strulovici, Bruno; Szydlowski, Martin;

doi: 10.2139/ssrn.1996808

handle: 10419/59687

On the Smoothness of Value Functions

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Abstract

We prove that under standard Lipschitz and growth conditions, the value function of all optimal control problems for one-dimensional diffusions is twice 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 differentiable.

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Germany

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Keywords

ddc:330, Dynamic Analysis, Stochastic Control, Super Contact, Smooth Pasting, Value Function, Super Contact; Smooth Pasting; HJB Equation; Optimal Control; Markov Control; Comparative Statics; Supermodularity; Single-Crossing; Interval Dominance Order, C61, C62, Super Contact, Value Function, Smooth Pasting, C61 - Optimization Techniques, Programming Models, Stochastic Control, jel: jel:C61

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