We develop the stochastic Perron 's method (see e.g. arXiv: 1212.2170) in the framework of stochastic target games (arXiv: 1307.5606) , in which one player tries to find a strategy such that the state process almost-surely reaches a given target no matter which action is chosen by the other player. Within this framework, the stochastic Perron's method produces a viscosity sub-solution (super-solution) of a Hamilton-Jacobi-Bellman (HJB) equation. Using a comparison result, we characterize the value  as a viscosity solution to the HJB equation  .
We extend the stochastic Perron method to analyze the framework of stochastic target games , in which one player tries to find a strategy such that the state process almost surely reaches a given target no matter which action is chosen by the other player. Within this framework, our method produces a viscosity sub-solution (super-solution) of a Hamilton-Jacobi-Bellman (HJB) equation. We then characterize the value function as a viscosity solution to the HJB equation using a comparison result and a byproduct to obtain the dynamic programming principle .
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(arXiv: 1307.5606)
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almost-surely
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the stochastic Perron's
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Using a comparison result, we
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using a comparison result and a byproduct to obtain the dynamic programming principle