On the smoothness of value functions and the existence of optimal strategies in diffusion models

Bruno Strulovici and Martin Szydlowski

Journal of Economic Theory, 2015, vol. 159, issue PB, 1016-1055

Abstract: Studies of dynamic economic models often rely on each agent having a smooth value function and a well-defined optimal strategy. For time-homogeneous optimal control problems with a one-dimensional diffusion, we prove that the corresponding value function must be twice continuously differentiable under Lipschitz, growth, and non-vanishing-volatility conditions. Under similar conditions, the value function of any optimal stopping problem is shown to be (once) continuously differentiable. We also provide sufficient conditions, based on comparative statics and differential methods, for the existence of an optimal control in the sense of strong solutions. The results are applied to growth, experimentation, and dynamic contracting settings.

Keywords: Optimal control; Optimal stopping; Smooth pasting; Super contact; Markov control; HJB equation (search for similar items in EconPapers)
JEL-codes: C61 C73 D86 O40 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (28)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:159:y:2015:i:pb:p:1016-1055

DOI: 10.1016/j.jet.2015.03.015

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