Making Decisions under Model Misspecification & Star-shaped Risk Measures - Maccheroni & Marinacci

Prof. Fabio Maccheroni & Prof. Massimo Marinacci - Making Decisions under Model Misspecification & Star-shaped Risk Measures

Making Decisions under Model Misspecification (45min)

Authors

Simone Cerreia-Vioglio, Lars Peter Hansen, Fabio Maccheroni, Massimo Marinacci

Abstract

We use decision theory to confront uncertainty that is sufficiently broad to incorporate "models as approximations." We presume the existence of a featured collection of what we call "structured models" that have explicit substantive motivations. The decision maker confronts uncertainty through the lens of these models, but also views these models as simplifications, and hence, as misspecified. We extend the max-min analysis under model ambiguity to incorporate the uncertainty induced by acknowledging that the models used in decision-making are simplified approximations. Formally, we provide an axiomatic rationale for a decision criterion that incorporates model misspecification concerns.

Star-shaped Risk Measures (15min)

Authors

Erio Castagnoli, Giacomo Cattelan, Fabio Maccheroni, Claudio Tebaldi, Ruodu Wang

Abstract

In this paper monetary risk measures that are positively super-homogeneous, called "star-shaped risk measures," are characterized and their properties studied. The measures in this class, which arise when the controversial subadditivity property of coherent risk measures is dispensed with and positive homogeneity is weakened, include both convex risk measures and Value-at-Risk (together with its robustifications). From a financial viewpoint, our relaxation of convexity is necessary to quantify the capital requirements for risk exposure in the presence of competitive delegation mechanisms. From a decision theoretical perspective, star-shaped risk measures emerge from variational preferences when risk mitigation strategies can be adopted by a rational decision maker.
A workshop to commemorate the centenary of publication of Frank Knight’s "Risk, Uncertainty, and Profit" and John Maynard Keynes’ “A Treatise on Probability”

This workshop is organised by the University of Oxford and supported by The Alan Turing Institute. For further details and regular updates, please visit the official event website

About the event
The year 2021 marks the centenary of two monumental publications in economics and probability theory, namely Risk, Uncertainty, and Profit by Frank Hyneman Knight and A Treatise on Probability by John Maynard Keynes.

In Risk, Uncertainty, and Profit, Knight put forward the vital difference between risk, where empirical evaluation of unknown outcomes can still be applicable, and uncertainty, where no quantified measurement is valid but subjective estimate. In A Treatise on Probability, Keynes argued that the concept of probability should be about the logical implication from premises to hypotheses, in contrast to the classical quantified perspective of probability.

The fundamental uncertainty proposed in both works has then deeply influenced the development of economic and probability theory in the past century and it still resonates with our lives today, considering the ups and downs that the world economy is experiencing.

This workshop is a tribute to their invaluable legacy.

Speakers:
Professor Dr Francesca Biagini, Ludwig Maximilian University of Munich
Professor Sara Biagini, LUISS Guido Carli
Professor Simon Blackburn, Trinity College, Cambridge
Professor Dr Paul Embrechts, ETH Zurich
Professor Itzhak Gilboa, HEC Paris
Professor Lars Hansen, University of Chicago
Professor Fabio Maccheroni, Bocconi University
Professor Massimo Marinacci, Bocconi University
Professor Marcel Nutz, Columbia University
Professor Shige Peng, Shandong University
Professor Dr Frank Riedel, Bielefeld University
Professor Ross Emmett, Arizona State University
Organizers:
Sam Cohen, Lars Hansen, Tomasz R. Bielecki, Igor Cialenco, Mike Tehranchi and Haoyang Cao

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