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Impulse Control of a Diffusion with a Change Point

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  • Lokman A. Abbas-Turki
  • Ioannis Karatzas
  • Qinghua Li

Abstract

This paper solves a Bayes sequential impulse control problem for a diffusion, whose drift has an unobservable parameter with a change point. The partially-observed problem is reformulated into one with full observations, via a change of probability measure which removes the drift. The optimal impulse controls can be expressed in terms of the solutions and the current values of a Markov process adapted to the observation filtration. We shall illustrate the application of our results using the Longstaff-Schwartz algorithm for multiple optimal stopping times in a geometric Brownian motion stock price model with drift uncertainty.

Suggested Citation

  • Lokman A. Abbas-Turki & Ioannis Karatzas & Qinghua Li, 2014. "Impulse Control of a Diffusion with a Change Point," Papers 1404.1761, arXiv.org.
    • Handle: RePEc:arx:papers:1404.1761
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    References listed on IDEAS

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    1. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    2. Bruno Bouchard & Ivar Ekeland & Nizar Touzi, 2004. "On the Malliavin approach to Monte Carlo approximation of conditional expectations," Finance and Stochastics, Springer, vol. 8(1), pages 45-71, January.
    3. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    4. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    5. Bernard Lapeyre & Emmanuel Temam, 2001. "Competitive Monte Carlo methods for the pricing of Asian options," Post-Print hal-01667057, HAL.
    6. repec:dau:papers:123456789/1802 is not listed on IDEAS
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    Cited by:

    1. Fontana, Claudio & Grbac, Zorana & Jeanblanc, Monique & Li, Qinghua, 2014. "Information, no-arbitrage and completeness for asset price models with a change point," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3009-3030.

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