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A Bayesian-martingale approach to the general disorder problem

Author

Listed:
  • Kavtaradze, T.
  • Lazrieva, N.
  • Mania, M.
  • Muliere, P.

Abstract

We consider a Bayesian-martingale approach to the general change-point detection problem. In our setting the change-point represents a random time of bifurcation of two probability measures given on the space of right-continuous functions. We derive a reflecting backward stochastic differential equation (RBSDE) for the value process related to the disorder problem and show that in classical cases of the Wiener and Poisson disorder problems this RBSDE is equivalent to free-boundary problems for parabolic differential and differential-difference operators respectively.

Suggested Citation

  • Kavtaradze, T. & Lazrieva, N. & Mania, M. & Muliere, P., 2007. "A Bayesian-martingale approach to the general disorder problem," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1093-1120, August.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:8:p:1093-1120
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    References listed on IDEAS

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    1. Dayanik, Savas & Karatzas, Ioannis, 2003. "On the optimal stopping problem for one-dimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 173-212, October.
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    Cited by:

    1. S. Cawston & L. Vostrikova, 2010. "$F$-divergence minimal equivalent martingale measures and optimal portfolios for exponential Levy models with a change-point," Papers 1004.3525, arXiv.org, revised Jun 2011.

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