Strulovici, Bruno and Szydlowski, Martin (2012): 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 onedimensional 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.
Item Type:  MPRA Paper 

Original Title:  On the Smoothness of Value Functions 
Language:  English 
Keywords:  Super Contact; Smooth Pasting; HJB Equation; Optimal Control; Markov Control; Comparative Statics; Supermodularity; SingleCrossing; Interval Dominance Order 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61  Optimization Techniques; Programming Models; Dynamic Analysis 
Item ID:  36326 
Depositing User:  Bruno Strulovici 
Date Deposited:  01. Feb 2012 07:26 
Last Modified:  19. Feb 2013 11:04 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/36326 