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Distributional Transforms, Probabilty Distortions, and Their Applications

In this paper we provide a general mathematical framework for distributional transforms, which allows for many examples that are used extensively in the literature of finance, economics, and optimization. We put a special focus on the class of probability distortions, which is a fundamental tool in decision theory. As our main results, we characterize distributional transforms satisfying various properties, and this includes an equivalent set of conditions which forces a distributional transform to be a probability distortion. As the first application, we construct new risk measures using distributional transforms. Sufficient and necessary conditions are given to ensure the convexity or coherence of the generated risk measures. In the second application, we introduce a new method for sensitivity analysis of risk measures based on composition groups of probability distortions. Finally, we construct probability distortions describing a change of measures with an example in option pricing.

Ketersediaan

Informasi Detail

Judul Seri

MATHEMATICS OF OPERATIONS RESEARCH; Vol.46 No.4 November 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1490-1512

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

VALUE-AT-RISK
OPTION PRICING
SENSITIVITY ANALYSIS
RISK MEASURES
EXPECTED SHORTFALL
DISTRIBUTIONAL TRANSFORMS
PROBABILITY DISTORTIONS
COMPOSITION GROUPS
CHANGE OF MEASURES

Info Detail Spesifik

https://doi.org/10.1287/moor.2020.1090

Pernyataan Tanggungjawab

Peng Liu, Alexander Schield, Ruondo Wang

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