Skip to main content
SpringerLink
Log in

A Class of Solvable Multiple Entry Problems with Forced Exits

  • Published:
Applied Mathematics & Optimization Submit manuscript

Abstract

We study an optimal investment problem with multiple entries and forced exits. A closed form solution of the optimisation problem is presented for general underlying diffusion dynamics and a general running payoff function in the case when forced exits occur on the jump times of a Poisson process. Furthermore, we allow the investment opportunity to be subject to the risk of a catastrophe that can occur at the jumps of the Poisson process. More precisely, we attach IID Bernoulli trials to the jump times and if the trial fails, no further re-entries are allowed. Interestingly, we find in the general case that the optimal investment threshold is independent of the success probability is the Bernoulli trials. The results are illustrated with explicit examples.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Borodin, A., Salminen, P.: Handbook on Brownian Motion—Facts and Formulae. 2 edn. (corrected 2 printing). Birkhäuser, Basel (2015)

  2. Bronstein, A.L., Zervos, M.: Sequential entry and exit decisions with an ergodic performance criterion. Stochastics 78(2), 99–121 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Campolieti, G., Makarov, R.N.: On properties of analytically solvable families of local volatility diffusion models. Math. Finance 22(3), 488–518 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chung, K.L., Walsh, J.B.: Markov Processes, Brownian Motion and Time Symmetry. Springer, New York (2005)

    Book  MATH  Google Scholar 

  5. Diamond, D.W., Rajan, R.G.: Liquidity risk, liquidity creation, and financial fragility: a theory of banking. J. Polit. Econ. 109, 287–327 (2001)

    Article  Google Scholar 

  6. Dixit, A.K.: Entry and exit decisions under uncertainty. J. Polit. Econ. 97, 620–638 (1989)

    Article  Google Scholar 

  7. Dixit, A.K., Pindyck, R.S.: Investment Under Uncertainty. Princeton University Press, Princeton (1994)

    Google Scholar 

  8. Duckworth, J.K., Zervos, M.: An investment model with entry and exit decisions. J. Appl. Probab. 37, 547–559 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dynkin, E.: Markov Processes I. Springer, Berlin (1965)

    Book  MATH  Google Scholar 

  10. Göing-Jaeschke, A., Yor, M.: A survey and some generalizations of Bessel processes. Bernoulli 9(2), 313–349 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lempa, J.: Optimal stopping with information constraint. Appl. Math. Optim. 66(2), 147–173 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ross, S.M.: Introduction to Probability Models, 10th edn. Academic Press, Los Angeles (2010)

    MATH  Google Scholar 

  13. Wang, H.: A sequential entry problem with forced exits. Math. Oper. Res. 30(2), 501–520 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zervos, M.: A problem of sequential entry and exit decisions combined with discretionary stopping. SIAM J. Control Optim. 42(2), 397–421 (2003)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

An anonymous referee is acknowledged for careful reading and a number of comments that led to a significant improvement of the paper. Paavo Salminen is acknowledged for helpful discussions.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Turku, FI - 20014, Turku, Finland

    Jukka Lempa

Authors
  1. Jukka Lempa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jukka Lempa.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lempa, J. A Class of Solvable Multiple Entry Problems with Forced Exits. Appl Math Optim 79, 593–619 (2019). https://doi.org/10.1007/s00245-017-9449-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00245-017-9449-6

Search

Navigation