Optimal statistical decisions about some alternative financial models
Stummer W, Vajda I (2007)
Publication Status: Published
Publication Type: Journal article
Publication year: 2007
Journal
Publisher: ELSEVIER SCIENCE SA
Book Volume: 137
Pages Range: 441-471
Journal Issue: 2
DOI: 10.1016/j.jeconom.2005.10.001
Abstract
We study Neyman-Pearson testing and Bayesian decision making based on observations of the price dynamics (X-1 : t is an element of [0, T]) of a financial asset, when the hypothesis is the classical geometric Brownian motion with a given constant growth rate and the alternative is a different random diffusion process with a given, possibly price-dependent, growth rate. Examples of asset price observations are introduced and used throughout the paper to demonstrate the applicability of the theory. By a rigorous mathematical approach, we obtain exact formulae and bounds for the most common statistical characteristics of testing and decision making, such as the power of test (type II error probability), the Bayes factor and its moments (power divergences), and the Bayes risk or Bayes error. These bounds can be much more easily evaluated than the exact formulae themselves and, consequently, they are useful for practical applications. An important theoretical conclusion of this paper is that for the class of alternatives considered neither the risk nor the errors converge to zero faster than exponentially in the observation time T. We illustrate in concrete decision situations that the actual rate of convergence is well approximated by the bounds given in the paper. (C) 2006 Elsevier B.V. All rights reserved.
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APA:
Stummer, W., & Vajda, I. (2007). Optimal statistical decisions about some alternative financial models. Journal of Econometrics, 137(2), 441-471. https://dx.doi.org/10.1016/j.jeconom.2005.10.001
MLA:
Stummer, Wolfgang, and Igor Vajda. "Optimal statistical decisions about some alternative financial models." Journal of Econometrics 137.2 (2007): 441-471.
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