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arXiv · 1212.2170

Stochastic Perron's method for Hamilton-Jacobi-Bellman equations

Erhan Bayraktar·Mihai Sirbu
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Abstract

We show that the value function of a stochastic control problem is the unique solution of the associated Hamilton-Jacobi-Bellman (HJB) equation, completely avoiding the proof of the so-called dynamic programming principle (DPP). Using Stochastic Perron's method we construct a super-solution lying below the value function and a sub-solution dominating it. A comparison argument easily closes the proof. The program has the precise meaning of verification for viscosity-solutions, obtaining the DPP as a conclusion. It also immediately follows that the weak and strong formulations of the stochastic control problem have the same value. Using this method we also capture the possible face-lifting phenomenon in a straightforward manner.

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BibTeXRIS

Erhan Bayraktar, Mihai Sirbu. 2012-12-10. Stochastic Perron's method for Hamilton-Jacobi-Bellman equations. https://arxiv.org/abs/1212.2170

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