Optimal stopping times for solutions of nonlinear stochastic differential equations and their application to one problem of financial mathematics |
| |
| Authors: | Yu S Mishura Ya O Ol'tsik |
| |
| Institution: | (1) Institute of Mathematics of Ukrainian National Academy of Sciences, 01601 Kyiv, Ukraine;(2) Department of Mathematical Analysis Faculty of Mechanics and Mathematics, National Taras Shevchenko University of Kyiv, 01033 Kyiv, Ukraine;(3) Department of Probability Theory and Mathematical Statistics Faculty of Mechanics and Mathematics, National Taras Shevchencko University of Kyiv, 01033 Kyiv, Ukraine |
| |
| 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
.
Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 6, pp. 804–809, June, 1999. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
