Parameter Estimation and Reverse Martingales


Posted: 24 Apr 1998

See all articles by Tomas Bjork

Tomas Bjork

Stockholm School of Economics - Swedish House of Finance

Bjorn Johansson

Stockholm University

Date Written: Undated


Within the framework of transitive sufficient processes we investigate identifiability properties of unknown parameters. In particular we consider unbiased parameter estimators, which are shown to be closely connected to time reversal and to reverse martingales. One of the main results is that, within our framework, every unbiased estimator process is a reverse martingale, thus automatically giving us strong consistency results. We also study structural properties of unbiased estimators, and it is shown that the existence of an unbiased parameter estimator is equivalent to the existence of a solution to an inverse boundary value problem. We give explicit representation formulas for the estimators in terms of Feynman-Kac type representations using complex valued diffusions, and we also give Cram=E9r-Rao bounds for the estimation error.

JEL Classification: C13

Suggested Citation

Bjork, Tomas and Johansson, Bjorn, Parameter Estimation and Reverse Martingales (Undated). WPS79-10/95, Available at SSRN:

Tomas Bjork (Contact Author)

Stockholm School of Economics - Swedish House of Finance ( email )

Drottninggatan 98
111 60 Stockholm

Bjorn Johansson

Stockholm University

Universitetsvägen 10
Stockholm, Stockholm SE-106 91
+46 8 162000, 6747000 (Phone)
+46 8 159522 (Fax)

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