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2006•Mathematical FinanceRequires access

DISTRIBUTION‐INVARIANT RISK MEASURES, INFORMATION, AND DYNAMIC CONSISTENCY

Stefan Weber

Open publisher page 246 citations

Abstract

In the first part of the paper, we characterize distribution‐invariant risk measures with convex acceptance and rejection sets on the level of distributions. It is shown that these risk measures are closely related to utility‐based shortfall risk. In the second part of the paper, we provide an axiomatic characterization for distribution‐invariant dynamic risk measures of terminal payments. We prove a representation theorem and investigate the relation to static risk measures. A key insight of the paper is that dynamic consistency and the notion of “measure convex sets of probability measures” are intimately related. This result implies that under weak conditions dynamically consistent dynamic risk measures can be represented by static utility‐based shortfall risk.

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What this paper is about

In the first part of the paper, we characterize distribution‐invariant risk measures with convex acceptance and rejection sets on the level of distributions. It is shown that these risk measures are closely related to utility‐based shortfall risk. In the second part of the paper, we provide an axiomatic characterization for distribution‐invariant dynamic risk measures of terminal payments. We prove a representation theorem and investigate the relation to static risk measures. A key insight of the paper is that dynamic consistency and the notion of “measure convex sets of probability measures” are intimately related. This result implies that under weak conditions dynamically consistent dynamic risk measures can be represented by static utility‐based shortfall risk.

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OpenAlex reports 246 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In the first part of the paper, we characterize distribution‐invariant risk measures with convex acceptance and rejection sets on the level of distributions. It is shown that these risk measures are closely related to utility‐based shortfall risk. In the second part of the paper, we provide an axiomatic characterization for distribution‐invariant dynamic risk measures of terminal payments. We prove a representation theorem and investigate the relation to static risk measures. A key insight of the paper is that dynamic consistency and the notion of “measure convex sets of probability measures” are intimately related. This result implies that under weak conditions dynamically consistent dynamic risk measures can be represented by static utility‐based shortfall risk.

Key concepts: Time consistency, Risk measure, Coherent risk measure, Econometrics, Dynamic risk measure, Mathematics, Regular polygon, Consistency (knowledge bases)

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