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arXiv · 1706.06824

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

Viorel Barbu·Chiara Benazzoli·Luca Di Persio
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Abstract

We show via the nonlinear semigroup theory in $L^1(\mathbb{R})$ that the $1$-D dynamic programming equation associated with a stochastic optimal control problem with multiplicative noise has a unique mild solution $\varphi\in C([0,T];W^{1,\infty}(\mathbb{R}))$ with $\varphi_{xx}\in C([0,T];L^1(\mathbb{R}))$. The $n$-dimensional case is also investigated.

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Viorel Barbu, Chiara Benazzoli, Luca Di Persio. 2017-06-21. Mild solutions to the dynamic programming equation for stochastic optimal control problems. https://arxiv.org/abs/1706.06824

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