Skip to main content
SpringerLink
Log in

Smallest g-supersolution with constraint

  • Published:
Applied Mathematics-A Journal of Chinese Universities Aims and scope Submit manuscript

Abstract

In this paper the existence and uniqueness of the smallest g-supersolution for BSDE is discussed in the case without Lipschitz condition imposing on both constraint function and drift coefficient in the different method from the one with Lipschitz condition. Then by considering (ξ, g) as a parameter of BSDE, and (ξ α, g α) as a class of parameters for BSDE, where α belongs to a set

, for every

there exists a pair of solution {Y a, Za} for the BSDE, the properties of

which is also a solution for some BSDE is studied. This result may be used to discuss optimal problems with recursive utility.

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. Cox, J., Ross, S., The valuation of options for alternative stochastic processes, J. of Finan. Econom., 1976, 3:145–166.

    Article  Google Scholar 

  2. Harrison, J. M., Kreps, D. M., Martingales and arbitrage in multi-period security markets, J. Econom. Theory, 1979, 20:381–408.

    Article  MATH  Google Scholar 

  3. Karatzas, I., Optimazation problems in the theory of continuous trading, SIAM J. Control Optim., 1989, 27 (6):1221–1259.

    Article  MATH  Google Scholar 

  4. Cvitanic, J., Karatzas, I., Hedging contingent with constrained portfolios, Ann. Appl. Probab., 1993, 3 (3):652–681.

    MATH  Google Scholar 

  5. Peng, S., Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer’s type, Probability Theorem and Related Field, 1999, 1137:473–499.

    Article  Google Scholar 

  6. Mao, X., Adapted solution of backward stochastic differential equations with non-Lipschitz coefficients, Stochastic Process and their Application, 1995, 58:281–292.

    Article  MATH  Google Scholar 

  7. Cao, Z. G., Yan, J. A., A comparison theorem for solutions of backward differential equations, Advances in Mathematics (China), 1999, 28 (4):304–308.

    MATH  Google Scholar 

  8. Karoui, N. E. L., Peng, S., Quenez, M. C., Backward stochastic differential equations in finance, Mathematical Finance, 1997, 1:1–71.

    Article  Google Scholar 

  9. Follmer, H., Schweizer, M., Hedging of contingent claims under incomplete information, In: Davis, M. H. A. and Elliot, R. J., eds., Applied Stochastic Analysis, London, Gordon and Breach 1991, 5:389–414.

    Google Scholar 

  10. Jacka, S. D., A martingale representation result and an application to imcomplete financial markets, Math. Finance, 1992, 2:239–250.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and System Science, Shandong Univ., 250100, Jinan

    Lin Qingquan

Authors
  1. Lin Qingquan
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by NSFC (79790130)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Qingquan, L. Smallest g-supersolution with constraint. Appl. Math. Chin. Univ. 15, 289–296 (2000). https://doi.org/10.1007/s11766-000-0053-0

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11766-000-0053-0

1991 MR Subject Classification

Keywords

Search

Navigation