Author
I︠a︡. B. Rutit︠s︡kiĭ
Bio: I︠a︡. B. Rutit︠s︡kiĭ is an academic researcher. The author has contributed to research in topics: Convex polytope & Convex analysis. The author has an hindex of 1, co-authored 1 publications receiving 1519 citations.
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2,329 citations
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.
Abstract: We 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 we prove a corresponding extension of the representation theorem in terms of probability measures on the underlying space of scenarios. As a case study, we consider convex measures of risk defined in terms of a robust notion of bounded shortfall risk. In the context of a financial market model, it turns out that the representation theorem is closely related to the superhedging duality under convex constraints.
1,302 citations
Posted Content•
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.
Abstract: We 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 we prove a corresponding extension of the representation theorem in terms of probability measures on the underlying space of scenarios. As a case study, we consider convex measures of risk defined in terms of a robust not ion of bounded shortfall risk. In the context of a financial market model, it turns out that the representation theorem is closely related to the superhedging duality under convex constraints.
1,141 citations
TL;DR: In this article, the authors studied the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market and showed that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theory to hold true is the requirement that the asymptotic elasticity of the utility function is strictly less then one.
Abstract: The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theory to hold true is the requirement that the asymptotic elasticity of the utility function is strictly less then one. (author's abstract)
1,071 citations
Book•
01 Jan 1999TL;DR: In this paper, Donsker's theorem, metric entropy and inequalities, and the universal and uniform central limit theorems are discussed. But they do not consider the two-sample case, the bootstrap case, and confidence sets.
Abstract: Preface 1. Introduction: Donsker's theorem, metric entropy and inequalities 2. Gaussian measures and processes sample continuity 3. Foundations of uniform central limit theorems: Donsker classes 4. Vapnik-Cervonenkis combinatorics 5. Measurability 6. Limit theorems for Vapnik-Cervonenkis and related classes 7. Metric entropy, with inclusion and bracketing 8. Approximation of functions and sets 9. Sums in general Banach spaces and invariance principles 10. Universal and uniform central limit theorems 11. The two-sample case, the bootstrap, and confidence sets 12. Classes of sets or functions too large for central limit theorems Appendices Subject index Author index Index of notation.
697 citations