Optimal Control Problems for Stochastic Problems with Absorbing Regimes

In this note we formulate an optimality problem for Stochastic process with a regime absorbing state. We present a solution for this problem as a pair of differential equations that are recusrsively linked. As an application I obtain an analytical for the Merton portfolio problem in a case for a stock with certain default probability in case of a log utility. As far as I can tell this analytical solution hasn't appeared in the literature before

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Year of publication:	2023
Authors:	Kopeliovich, Yaacov
Publisher:	[S.l.] : SSRN
Subject:	Kontrolltheorie \| Control theory \| Stochastischer Prozess \| Stochastic process \| Mathematische Optimierung \| Mathematical programming

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