On the regularity of American options with regime-switching uncertainty

2013/09/05 by Jacka, S. D., Ocejo, A.
#35B65 #60G17 #60J70 (Primary) #60K37 #91G80 (Secondary) #93C30 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.1309.1404

Abstract

We study the regularity of the stochastic representation of the solution of a class of initial-boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal stopping problem such as the price of an American-style option in finance. We show continuity and smoothness of the value function using coupling and time-change techniques. As an application, we find the minimal payoff scenario for the holder of an American-style option in the presence of regime-switching uncertainty under the assumption that the transition rates are known to lie within level-dependent compact sets.

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