Coherent multiperiod risk adjusted values and Bellman’s principle
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In this article, a time-0 coherent risk measure is defined for value processes and two other constructions of measurement processes are given in terms of sets of test probabilities, when the sets fulfill a stability condition also met in multi-period treatment of ambiguity as in decision-making.Abstract:
Starting with a time-0 coherent risk measure defined for “value processes”, we also define risk measurement processes. Two other constructions of measurement processes are given in terms of sets of test probabilities. These latter constructions are identical and are related to the former construction when the sets fulfill a stability condition also met in multiperiod treatment of ambiguity as in decision-making. We finally deduce risk measurements for the final value of locked-in positions and repeat a warning concerning Tail-Value-at-Risk.read more
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References
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Journal ArticleDOI
Coherent Measures of Risk
TL;DR: In this paper, the authors present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent", and demonstrate the universality of scenario-based methods for providing coherent measures.
Journal ArticleDOI
MAxmin expected utility with non-unique prior
TL;DR: In this paper, the authors characterize preference relations over acts which have a numerical representation by the functional J(f) = min > {∫ uo f dP / P∈C } where f is an act, u is a von Neumann-Morgenstern utility over outcomes, and C is a closed and convex set of finitely additive probability measures on the states of nature.
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Convex measures of risk and trading constraints
Hans Föllmer,Alexander Schied +1 more
TL;DR: In this paper, the authors introduce the notion of a convex measure of risk, an extension of the concept of a coherent risk measure defined in Artzner et al. (1999), and prove a corresponding extension of representation theorem in terms of probability measures on the underlying space of scenarios.
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Convex measures of risk and trading constraints
Hans Föllmer,Alexander Schied +1 more
TL;DR: The notion of a convex measure of risk is introduced, an extension of the concept of a coherent risk measure defined in Artzner et al. (1999), and a corresponding extensions of the representation theorem in terms of probability measures on the underlying space of scenarios are proved.