Skip to main content
SpringerLink
Log in

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

  • Published:
Ukrainian Mathematical Journal Aims and scope

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 .

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. G. Fakeev, “On optimal stopping of processes with continuous time”,Teor. Ver. Primen.,15, No. 2, 336–344 (1970).

    MATH  MathSciNet  Google Scholar 

  2. L. I. Gal'chuk, “Comparison theorem for stochastic equations with integrals over martingales and random measures”,Teor. Ver. Primen.,27, No. 3, 425–433 (1982).

    MathSciNet  Google Scholar 

  3. I. I. Gikhman and A. V. SkorokhodStochastic Differential Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1982).

    MATH  Google Scholar 

  4. M. Brodie and J. Detemple, “The valuation of American options on multiple assets”,Math. Finance,7, No. 3, 241–286 (1997).

    Article  MathSciNet  Google Scholar 

Download references

Authors
  1. Yu. S. Mishura
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ya. O. Ol'tsik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 6, pp. 804–809, June, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02591977

Keywords

Search

Navigation