Optimal stopping times for solutions of nonlinear stochastic differential equations and their application to one problem of financial mathematics

  • Yu. S. Mishura Київ. нац. ун-т iм. Т. Шевченка
  • Ya. O. Oltsik


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 .
How to Cite
Mishura, Y. S., and Y. O. Oltsik. “Optimal Stopping Times for Solutions of Nonlinear Stochastic Differential Equations and Their Application to One Problem of Financial Mathematics”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 51, no. 6, June 1999, pp. 804–809, https://umj.imath.kiev.ua/index.php/umj/article/view/4667.
Research articles