Skip to main content
SpringerLink
Log in

Risk sensitive impulse control of non-Markovian processes

  • Original Article
  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

Abstract

We consider the problem of an optimal stochastic impulse control of non-Markovian Processes when the expression of the cost functional integrates sensitiveness with respect to the risk. For this class, we try to establish the existence of an optimal strategy. We prove that our impulse control problem could be reduced to an iterative sequence of optimal stopping ones. Basically, the problem is solved using techniques involving the Snell envelope notion.

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

  • Baccarin S, Sanfelici S (2006) Optimal impulse control on an unbounded domain with nonlinear cost functions. Comput Manag Sci 3: 81–100

    Article  MathSciNet  MATH  Google Scholar 

  • Bensoussan A, Lions JL (1984) Impulse control and quasivariational inequalities. Gauthier-Villars, Montrouge

    Google Scholar 

  • Cadenillas A, Zapatero F (2000) Classical and impulse stochastic control of the exchange rate using interest rates and reserves. Math Finan 10(2): 141–156

    Article  MathSciNet  MATH  Google Scholar 

  • Chancelier JP, Øksendal B, Sulem A (2001) Combined stochastic control and optimal stopping, and application to numerical approximation of combined stochastic and impulse control. Stochastic Financial Mathematics, Proc. Steklov Math. Institute, Moscow pp 149–175

  • Djehiche B, Hamadène S, Hdhiri I (2008) Stochastic impulse control of Non-Markovian Processes. Appl Math Optim, doi:10.1007/s00245-009-9070-4

  • El-Karoui N (1981) Les aspects probabilistes du contrôle stochastique Ecole d’été de Saint-Flour. Lecture notes in mathematics, vol 876. Springer, Berlin, pp 73–238

  • Hamadène S (2002) Reflected BSDEs with discontinuous barrier and applications. Stoch Stoch Rep 74(3–4): 571–596

    MathSciNet  MATH  Google Scholar 

  • Karatzas I, Shreve S E (1998) Methods of mathematical finance, applications of mathematics, vol 39. Springer, New York

    Google Scholar 

  • Menaldi JL (1980) On the optimal impulse control problem for degenerate diffusions. SIAM J Cont Opt 18(6): 722–739

    Article  MathSciNet  MATH  Google Scholar 

  • Shiryayev AN (1978) Optimal stopping rules. Springer, New York

    MATH  Google Scholar 

  • Stettner L (1989) On some stopping and impulsive control problems with a general discount rate criterion. Probab Math Stat 10: 145–245

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculté de Sciences de Gabès & URMAPM, Gabès, Tunisie

    Ibtissam Hdhiri

  2. Université 7 nouvembre de Carthage, Unité de recherche, Analyse Stochastique et Modélisation Statistique, Gabès, Tunisie

    Monia Karouf

Authors
  1. Ibtissam Hdhiri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Monia Karouf
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ibtissam Hdhiri.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hdhiri, I., Karouf, M. Risk sensitive impulse control of non-Markovian processes. Math Meth Oper Res 74, 1–20 (2011). https://doi.org/10.1007/s00186-010-0338-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00186-010-0338-x

Keywords

Mathematics Subject Classification (2000)

Search

Navigation