Risk Measures in the Form of Infimal Convolution

Kirilyuk, V. S.

doi:10.1007/s10559-021-00327-z

Cybern Syst Anal

2021

DOI: 10.1007/s10559-021-00327-z

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Risk Measures in the Form of Infimal Convolution

V. S. Kirilyuk

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Cited by 2 publications

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Inf-convolution and optimal risk sharing with countable sets of risk measures

Righi

Moresco

2022

Ann Oper Res

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We introduce the concept of set risk measures (SRMs), which are real-valued maps defined on the space of all non-empty, closed, and bounded sets of almost surely bounded random variables. Traditional risk measures typically operate on spaces of random variables, but SRMs extend this framework to sets of random variables. We establish an axiom scheme for SRMs, similar to classical risk measures but adapted for set operations. The main technical contribution is an axiomatic dual representation of convex SRMs by using regular, finitely additive measures on the unit ball of the dual space of essentially bounded random variables. We explore worst-case SRMs, which evaluate risk as the supremum of individual risks within a set, and provide a collection of examples illustrating the applicability of our framework to systemic risk, portfolio optimization, and decision-making under uncertainty. This work extends the theory of risk measures to a more general and flexible setup, accommodating a broader range of financial and mathematical applications.

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Inf-convolution and optimal risk sharing with countable sets of risk measures

Righi

Moresco

2022

Ann Oper Res

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Polyhedral Coherent Risk Measure and Distributionally Robust Portfolio Optimization

Kirilyuk

2023

Cybern Syst Anal

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Risk Measures in the Form of Infimal Convolution

Cited by 2 publications

References 19 publications

Inf-convolution and optimal risk sharing with countable sets of risk measures

Inf-convolution and optimal risk sharing with countable sets of risk measures

Polyhedral Coherent Risk Measure and Distributionally Robust Portfolio Optimization

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