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A free boundary problem connected with the optimal stopping problem for diffusion processes


Author: Daniel B. Kotlow
Journal: Trans. Amer. Math. Soc. 184 (1973), 457-478
MSC: Primary 60J60; Secondary 35K20
MathSciNet review: 0365729
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Abstract: This paper deals with a free boundary problem for a parabolic equation in one space variable which arises from the problem of selecting an optimal stopping strategy for the diffusion process connected with the equation. It is shown that a solution of the free boundary problem yields the solution of a minimum problem concerning supersolutions of the parabolic equation as well as the solution of the optimal stopping problem. Theorems regarding the existence, uniqueness, regularity, and approach to the steady state of solutions of the free boundary problem are established.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0365729-0
Keywords: Free boundary problem, parabolic equation, minimal supersolution, optimal stopping, diffusion process, optimal stochastic control
Article copyright: © Copyright 1973 American Mathematical Society