Quantifying Ambiguity Bounds Through Hypothetical Statistical Testing

27 Pages Posted: 22 Dec 2015 Last revised: 3 Dec 2018

See all articles by Anne Balter

Anne Balter

Tilburg University; Netspar

Antoon Pelsser

Maastricht University; Netspar

Multiple version iconThere are 2 versions of this paper

Date Written: October 11, 2018

Abstract

Models can be wrong and recognising their limitations is important in financial and economic decision making under uncertainty. Robust strategies, which are least sensitive to perturbations of the underlying model, take uncertainty into account. Finding the explicit set of alternative models surrounding the baseline model has been difficult so far. We specify alternative models by a stochastic change of probability measure and derive a quantitative bound on the uncertainty set. We find an explicit ex ante relation between the choice parameter k, which is the radius of the uncertainty set, and the Type I and II error probabilities on the statistical test that is hypothetically performed to investigate whether the model specification is still appropriate at the future test horizon. The hypothetical test is constructed to obtain all alternative models that cannot be distinguished from the baseline model with enough power. Moreover, we also link the bound k, which is now a function of interpretable variables, to numerical values on several divergence measures. Finally, we illustrate the methodology on a robust investment problem and identify how the robustness multiplier can be numerically interpreted by ascribing meaning to the amount of ambiguity.

Keywords: Model uncertainty, robustness, stochastic control, optimisation, misspecification, divergence, investment problem

JEL Classification: C00, D81, G11

Suggested Citation

Balter, Anne and Pelsser, Antoon A. J., Quantifying Ambiguity Bounds Through Hypothetical Statistical Testing (October 11, 2018). Netspar Discussion Paper No. 11/2015-038, Available at SSRN: https://ssrn.com/abstract=2706610 or http://dx.doi.org/10.2139/ssrn.2706610

Anne Balter (Contact Author)

Tilburg University ( email )

P.O. Box 90153
Tilburg, DC Noord-Brabant 5000 LE
Netherlands

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Antoon A. J. Pelsser

Maastricht University ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

HOME PAGE: http://https://sites.google.com/site/apelsseraca/

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

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