Mimicking and Conditional Control with Hard Killing

2024/09/16 by Carmona, Rene, Lacker, Daniel · 2 citations
#60H10 #60J60 #93E20 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2409.10650

Abstract

We first prove a mimicking theorem (also known as a Markovian projection theorem) for the marginal distributions of an Ito process conditioned to not have exited a given domain. We then apply this new result to the proof of a conjecture of P.L. Lions for the optimal control of conditioned processes.

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• Linking Path-Dependent and Stochastic Volatility Models
• Conditional McKean-Vlasov control

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