Abstract
To introduce Keynes’s Treatise on Probability in a short time I shall emphasize its remarkable scholarship; its debt to Russell’s logicism; and its pervasive scepticism about the possibility of applying mathematics to its subject. I then briefly consider the departure from logicism due to Frank Ramsey, and Keynes’s own generous, if unconvinced, reaction to Ramsey’s criticisms.
Speaker
Ross Emmett, Professor of Economic Thought, School of Civic and Economic Thought and Leadership, and Director, Center for the Study of Economic Liberty, Arizona State University
Abstract
Frank Knight’s Risk, Uncertainty and Profit was published in 1921, and has remained in publication ever since. After a brief biographical sketch of the author’s life, the paper turns to the two aspects of the book that kept it alive in the economics profession long after other doctoral dissertations published under the auspices of the Hart, Schaffner and Marx essay competition were forgotten. The first is Knight’s re-interpretation of price theory. It is Knight’s price theory that led Lionel Robbins to reprint Risk, Uncertainty and Profit from 1933 to the 1960s, and it is the price theory sections of the book that graduate students in the University of Chicago’s Department of Economics turned to for background on their professor’s ideas. The second is his use of uncertainty to elucidate a theory of imperfect competition in which uncertainty both leads to a variety of contractual relations that firm owners may make with suppliers, insurance providers, laborers, and hired managers, and brings increased uncertainty through principal/agent and incentive incompatibility problems. At the same, time, the dynamism of imperfect competition creates potential for innovation and new firm creation, which in turn challenges the existing social organization of economic activity.
Related Works
"The Writing and Reception of Risk, Uncertainty and Profit", forthcoming in the Cambridge Journal of Economics.
"What Can We Learn about Frank Knight's Economic Theory from the Prefaces to the Reprints of Risk, Uncertainty and Profit?", forthcoming in Research in the History of Economic Thought and Methodology.
"Uncertainty and the Social Organization of Economic Activity", forthcoming in the Journal of Institutional Economics.
Abstract
We live in a world filled with uncertainty. In this essay, I show that featuring this phenomenon more in economic analyses adds to our understanding of how financial markets work and how best to design prudent economic policy. This essay explores methods that allow for a broader conceptualization of uncertainty than is typical in economic investigations. These methods draw on insights from decision theory to engage in uncertainty quantification and sensitivity analysis. Uncertainty quantification in economics differs from most sciences because there is uncertainty both from the perspective of an external observer and from people and enterprises within the model. I illustrate these methods in two example economies in which the understanding of long-term growth is limited. One example looks at uncertainty ramifications for fluctuations in financial markets, and the other considers the prudent design of policy when the quantitative magnitude of climate change and its impact on economic opportunities is unknown.
References:
1) Hansen, Lars. "Uncertainty Spillovers for Markets and Policy"
2) Barnett, Michael, Brock, William, and Hansen, Lars. "Pricing Uncertainty Induced by Climate Change" The Review of Financial Studies, Volume 33, Issue 3, March 2020, Pages 1024–1066
3) Hansen, Lars and Sargent, Thomas J. "Macroeconomic uncertainty prices when beliefs are tenuous" Journal of Econometrics, 2020.
Abstract
This talk is based on the joint work with Prof. Larry Samuelson from the Department of Economics at Yale University and full text is available here.
Abstract
Abstract
Abstract
In this talk we present a market model including financial assets and life insurance liabilities within a reduced-form framework under model uncertainty by following [1]. In particular we extend this framework to include mortality intensities following an affine process under parameter uncertainty, as defined in [2]. This allows both to introduce the definition of a longevity bond under model uncertainty in a consistent way with the classical case under one prior, as well as to compute it by explicit formulas or by numerical methods. We also study conditions to guarantee the existence of a càdlàg modification for the longevity bond’s value process. Furthermore, we show how the resulting market model extended with the longevity bond is arbitrage-free and study arbitrage-free pricing of contingent claims or life insurance liabilities in this setting.
This talk is based on:
[1] Francesca Biagini and Yinglin Zhang. "Reduced-form framework under model uncertainty". The Annals of Applied Probability, 29(4):2481–2522, 2019.
[2] Francesca Biagini and Katharina Oberpriller. "Reduced-form framework under model uncertainty". Preprint University of Munich and Gran Sasso Science Institute, 2020.
[3] Tolulope Fadina, Ariel Neufeld, and Thorsten Schmidt. "Affine processes under parameter uncertainty". Probability, Uncertainty and Quantitative Risk, volume 4 (5), 2019.
Abstract
The talk will be a review of Knight's thoughts on uncertainty in economics and their influence on current studies in finance.
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.
Abstract
I will frame this talk in the context of what I refer to as the First and Second Fundamental Theorem of Quantitative Risk Management (1&2-FTQRM). An alternative subtitle for 1-FTQRM would be "Mathematical Utopia", for 2-FTQRM it would be "Wall Street Reality". I will mainly concentrate on uncertainty at the level of interdependence between risk factors and be interested in the derivation of extremal (inf-sup) bounds for risk measures, like Value-at-Risk and Expected Shortfall, of portfolios as functions of these factors.
Abstract
We present a robust version of the life-cycle optimal portfolio choice model with sticky wages introduced by Biffis, Gozzi and Prosdocimi. There, the influence of past wages on the future ones is modelled linearly in the evolution equation of labor income, through a given weight function. Their result passes through the resolution of an infinite-dimensional HJB equation. We improve the state of art in two ways. First, we allow the weight to be a Radon measure. This accommodates for more realistic weighting, like e.g. on a discrete temporal grid according to some periodic income. Second, we allow the weight to change with time, possibly lacking perfect identification. The uncertainty is specified by a given set of Radon measures K, in which the weighting process takes values. This renders the inevitable uncertainty on how the past affects the future, and includes the standard case of error bounds on a specific estimate for the weight. Under uncertainty averse preferences, the decision-maker takes a maximin approach to the problem. Our analysis confirms the intuition: in our infinite-dimensional setting, the optimal policy is the best investment strategy under the worst-case weight. The resolution is based on an infinite-dimensional HJB-Isaacs equation, which appears to be new in this context.