Abstract
We solve the problem of finding the optimal switching time for two alternative strategies at the financial market in the case where a random processX t ,t ∈ [0, T], describing an investor's assets satisfies a nonlinear stochastic differential equation. We determine this switching time τ∈[0,T] as the optimal stopping time for a certain processY t generated by the processX t so that the average investor's assets are maximized at the final time, i.e.,EX T .
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Additional information
Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 6, pp. 804–809, June, 1999.
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Mishura, Y.S., Ol'tsik, Y.O. Optimal stopping times for solutions of nonlinear stochastic differential equations and their application to one problem of financial mathematics. Ukr Math J 51, 899–906 (1999). https://doi.org/10.1007/BF02591977
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DOI: https://doi.org/10.1007/BF02591977