Introduction to Imprecise Probabilities

Chapter 12Financial risk measurement

Paolo Vicig

Department DEAMS ‘B. de Finetti’, University of Trieste, Italy

12.1 Introduction

The statement that the theory of imprecise probabilities offers potentially many applications in the realms of finance and economics should seem quite obvious to a reader with some general knowledge of the theory, for instance to someone acquainted with just the introductory chapters of this book. In fact, a strong motivation for introducing imprecise probabilities is that they avoid from the very beginning the difficulty of assessing precisely beliefs which might be more or less vague. This motivation applies to these areas of investigation too, perhaps to an even larger extent than in physics, engineering or other fields of knowledge, since measurement of the relevant quantities may be more imprecise, or rely more heavily upon subjective evaluations, feelings, etc. Any model in finance making use of precise probabilities (think for instance of option pricing models) could be generalized by choosing instead imprecise probabilities as uncertainty evaluations.

Further, recall from Chapter 2 that a lower prevision (alternatively, an upper prevision ) is itself interpreted as a supremum buying price (an infimum selling price) for the gamble . This provides ...