Emanuela Rosazza Gianin

Bio: Emanuela Rosazza Gianin is an academic researcher from University of Milano-Bicocca. The author has contributed to research in topics: Capital allocation line & Risk measure. The author has an hindex of 14, co-authored 45 publications receiving 1992 citations. Previous affiliations of Emanuela Rosazza Gianin include University of Milan.

Putting order in risk measures

Abstract: This paper introduces a set of axioms that define convex risk measures. Duality theory provides the representation theorem for these measures and the link with pricing rules.

Risk measures via g-expectations

Abstract: This paper shows how g -expectations and conditional g -expectations provide some families of static and dynamic risk measures. Conversely, some sufficient conditions for a dynamic risk measure to be induced by a conditional g -expectation are provided. A financial interpretation of the functional g will be given.

Generalized Quantiles as Risk Measures

Abstract: In the statistical and actuarial literature several generalizations of quantiles have been considered, by means of the minimization of a suitable asymmetric loss function. All these generalized quantiles share the important property of elicitability, that is recently receiving a lot of attention since it corresponds to the existence of a natural backtesting methodology. In this paper we investigate the case of M-quantiles, defined as the minimizers of an asymmetric convex loss function, in contrast to Orlicz quantiles, that have been considered in Bellini and Rosazza Gianin (2012). We discuss their properties as risk measures and point out the connection with the zero utility premium principle and with shortfall risk measures introduced by Follmer and Schied (2002). In particular, we show that the only M-quantiles that are coherent risk measures are the expectiles, introduced by Newey and Powell (1987) as the minimizers of an asymmetric quadratic loss function. We provide their dual and Kusuoka representations and discuss their relationship with CVaR. We analyze their asymptotic properties and show that for very heavy tailed distributions expectiles are more conservative than the usual quantiles. Finally, we show their robustness in the sense of lipschitzianity with respect to the Wasserstein metric.

Representation of the penalty term of dynamic concave utilities

Abstract: In the context of a Brownian filtration and with a fixed finite time horizon, we provide a representation of the penalty term of general dynamic concave utilities (hence of dynamic convex risk measures) by applying the theory of g-expectations.

Law invariant convex risk measures

Abstract: As a generalization of a result by Kusuoka (2001), we provide the representation of law invariant convex risk measures. Very particular cases of law invariant coherent and convex risk measures are also studied.

Quantitative Risk Management: Concepts, Techniques, and Tools

Abstract: This book provides the most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management. Whether you are a financial risk analyst, actuary, regulator or student of quantitative finance, Quantitative Risk Management gives you the practical tools you need to solve real-world problems. Describing the latest advances in the field, Quantitative Risk Management covers the methods for market, credit and operational risk modelling. It places standard industry approaches on a more formal footing and explores key concepts such as loss distributions, risk measures and risk aggregation and allocation principles. The book's methodology draws on diverse quantitative disciplines, from mathematical finance and statistics to econometrics and actuarial mathematics. A primary theme throughout is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. Proven in the classroom, the book also covers advanced topics like credit derivatives. Fully revised and expanded to reflect developments in the field since the financial crisis Features shorter chapters to facilitate teaching and learning Provides enhanced coverage of Solvency II and insurance risk management and extended treatment of credit risk, including counterparty credit risk and CDO pricing Includes a new chapter on market risk and new material on risk measures and risk aggregation

Precautionary Saving in the Small and in the Large

Abstract: The theory of precautionary saving is shown in this paper to be isomorphic to the Arrow-Pratt theory of risk aversion, making possible the application of a large body of knowledge about risk aversion to precautionary saving, and more generally, to the theory of optimal choice under risk In particular, a measure of the strength of precautionary saving motive analogous to the Arrow-Pratt measure of risk aversion is used to establish a number of new propositions about precautionary saving, and to give a new interpretation of the Oreze-Modigliani substitution effect

Convex measures of risk and trading constraints

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.

Nonlinear Expectations and Stochastic Calculus under Uncertainty

Abstract: In this book, we introduce a new approach of sublinear expectation to deal with the problem of probability and distribution model uncertainty. We a new type of (robust) normal distributions and the related central limit theorem under sublinear expectation. We also present a new type of Brownian motion under sublinear expectations and the related stochastic calculus of Ito's type. The results provide robust tools for the problem of probability model uncertainty arising from financial risk management, statistics and stochastic controls.