Mild solutions to the dynamic programming equation for stochastic optimal control problems

2017/06/21 by Viorel Barbu, Barbu, Viorel, Chiara Benazzoli +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1706.06824

arxiv created 2017/06/21 · arxiv updated 2017/06/22

Abstract

We show via the nonlinear semigroup theory in L¹(ℝ) that the 1-D dynamic programming equation associated with a stochastic optimal control problem with multiplicative noise has a unique mild solution φ∈ C([0,T];W^1,∞(ℝ)) with φ_xx∈ C([0,T];L¹(ℝ)). The n-dimensional case is also investigated.

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