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Adaptive prediction and reverse martingales

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  • Björk, Tomas
  • Johansson, Björn

Abstract

We study prediction problems for models where the underlying probability measure is not known. These problems are intimately connected with time reversal of Markov processes, and optimal predictors are shown to be characterized by being reverse martingales. For a class of diffusions we give a Feynman-Kac representation of the optimal predictor in terms of an associated complex valued diffusion and a concrete Wiener model is studied in detail. We also derive Cramér-Rao inequalities for the prediction error.

Suggested Citation

  • Björk, Tomas & Johansson, Björn, 1992. "Adaptive prediction and reverse martingales," Stochastic Processes and their Applications, Elsevier, vol. 43(2), pages 191-222, December.
    • Handle: RePEc:eee:spapps:v:43:y:1992:i:2:p:191-222
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    Cited by:

    1. Björk, Tomas & Johansson, Björn, 1996. "Parameter estimation and reverse martingales," Stochastic Processes and their Applications, Elsevier, vol. 63(2), pages 235-263, November.
    2. Raquel M. Gaspar & Mariana Khapko, 2023. "In memoriam: Tomas Björk (1947–2021)," Finance and Stochastics, Springer, vol. 27(4), pages 867-885, October.

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