Optimal stopping times for solutions of nonlinear stochastic differential equations and their application to one problem of financial mathematics - Mishura, Yu. S.; Oltsik, Ya. O. (Ukrains’kyi Matematychnyi Zhurnal, 1999)
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 .