Hans Föllmer - Academia.edu (original) (raw)
Papers by Hans Föllmer
Essays on the Nature and State of Modern Economics, 2015
ABSTRACT The fundamental failing of modern economics, or at least of its dominant mainstream proj... more ABSTRACT The fundamental failing of modern economics, or at least of its dominant mainstream project, is not that it was unable successfully to predict the recent crisis but that it is ill-equipped to illuminate much that happens in the economy at any time. The latter is an assessment that I have advanced and defended on numerous occasions (e.g., Lawson, 1997, 2003). Contemporary mainstream economics relies almost exclusively on certain methods of mathematical deductivist modelling; indeed it insists that formalistic modelling is the proper way to do economics. My contention, defended elsewhere at length, is simply that these methods are in fact largely irrelevant to addressing social reality, and it is the insistence that such methods be everywhere utilised that accounts for the continuing sorry intellectual state of much of the modern discipline. Recently, I advanced a framework of analysis that, I suggested, is generally relevant for social analysis, including understanding the nature of the recent 'crisis' (Lawson 2009a). In the course of developing the arguments of the paper containing that framework, I took the opportunity to critically reference a contribution by (2008). I did so because the latter paper appeared to me to send the signal that the crisis teaches us that we need to develop different versions of the mathematical models than those hitherto used to guide policy. Although the Colander et al (2008) paper, as might be expected from such a collection of authors, is insightful, the noted response, I believe, is not the best one. Because the paper seemed to have been influential, not least in heterodox circles, I used it as a kind of foil to set out my alternative account. I was, and remain, particularly concerned that the very recent apparent rise in popularity of seemingly radical substantive theories, most especially those that are counted as Keynesian, should not be used merely to develop alternative mathematical models to those previously dominant. If my arguments about the limitations of formalism are correct, it follows that the situation of modern economics represents a very significant misallocation of resources – almost all are given over to the mathematical modelling project. Yet the seriousness of this unhappy state of affairs seems still to go largely unappreciated. So when the editor of this journal, Edward Fullbrook, invited me to produce a short paper that covered some of the same ground as in Lawson (2009a), I was happy enough to comply. However the invite was rather unusual in its details. It proposed a debate of sorts between myself and Colander et al covering those particular aspects on which we appear to disagree. Further, this debate was to take the form not of a direct engagement but of each set of contributors marshalling or summarising arguments of our earlier papers to address the statement below formulated by Fullbrook himself. This then explains the orientation of what follows. The statement in question runs as follows.
RePEc: Research Papers in Economics, 2001
RePEc: Research Papers in Economics, 1999
An investor faced with a contingent claim may eliminate risk by super hedging in a financial mark... more An investor faced with a contingent claim may eliminate risk by super hedging in a financial market As this is often quite expensive we study partial hedges which require less capital and reduce the risk In a previous paper we determined quantile hedges which succeed with maximal probability given a capital constraint Here we look for strategies which minimize the shortfall risk defined as the expectation of the shortfall weighted by some loss function The resulting efficient hedges allow the investor to interpolate in a systematic way between the extremes of no hedge and a perfect super hedge depending on the accepted level of shortfall risk.
Annual Review of Financial Economics, 2015
The quantification of downside risk in terms of capital requirements is a key issue for both regu... more The quantification of downside risk in terms of capital requirements is a key issue for both regulators and the financial industry. This review presents the axiomatic approach, which is based on monetary risk measures. These provide a unifying mathematical framework for the determination of capital requirements, for economic indices of riskiness, and for the analysis of preferences in the face of risk and Knightian uncertainty. In the special case of distribution-based risk measures, we review recent advances in characterizing their statistical properties such as elicitability and robustness.
Séminaire de Probabilités IX Université de Strasbourg, 1975
Journal of Applied Probability, 1972
We discuss the potential theory of optimal stopping for a standard process and an unbounded rewar... more We discuss the potential theory of optimal stopping for a standard process and an unbounded reward function. This is applied to Brownian motion constrained to a N(m, σ2) distribution at time 1. Boyce [2] has discovered, via computer, various interesting features of this example. We provide direct proofs for some of them, in particular for the qualitative jump of the optimal strategy as the variance σ2 passes the critical value 1.
Lecture Notes in Mathematics, 1981
Finance and Stochastics, Feb 1, 2000
Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006, Nov 9, 2009
Annals of Probability, Feb 1, 1984
Mitteilungen der Deutschen mathematiker-Vereinigung, Sep 15, 2009
Stochastic Processes and their Applications, Nov 1, 2001
Springer eBooks, Oct 10, 2005
We introduce an entropy technique which allows to treat some infinite-dimensional extensions of t... more We introduce an entropy technique which allows to treat some infinite-dimensional extensions of the classical duality equations for the time reversal of diffusion processes.
Proceedings of symposia in pure mathematics, 1977
Springer eBooks, Feb 6, 2006
Birkhäuser Basel eBooks, 1998
Richard von Mises was professor at the University of Berlin from 1920 to 1933. During these thirt... more Richard von Mises was professor at the University of Berlin from 1920 to 1933. During these thirteen years he advanced, with great vigour, the field of applied mathematics and stochastics. His research contributions cover a most impressive range, and the impact of his ideas can be felt even today.
Birkhäuser Boston eBooks, 1990
Elsevier eBooks, 1991
Abstract Stochastic integrals with respect to a martingale X often involve a predictable process ... more Abstract Stochastic integrals with respect to a martingale X often involve a predictable process integrated against the continuous martingale component Xc together with terms which are integrals of the compensated random measures associated with the jumps. The latter are related to ‘optional’ stochastic integrals. The main result of this paper relates such a stochastic integral with the sum of a predictable stochastic integral of X and an orthogonal martingale. The result has applications in the hedging of contingent claims in finance.
Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1969
Essays on the Nature and State of Modern Economics, 2015
ABSTRACT The fundamental failing of modern economics, or at least of its dominant mainstream proj... more ABSTRACT The fundamental failing of modern economics, or at least of its dominant mainstream project, is not that it was unable successfully to predict the recent crisis but that it is ill-equipped to illuminate much that happens in the economy at any time. The latter is an assessment that I have advanced and defended on numerous occasions (e.g., Lawson, 1997, 2003). Contemporary mainstream economics relies almost exclusively on certain methods of mathematical deductivist modelling; indeed it insists that formalistic modelling is the proper way to do economics. My contention, defended elsewhere at length, is simply that these methods are in fact largely irrelevant to addressing social reality, and it is the insistence that such methods be everywhere utilised that accounts for the continuing sorry intellectual state of much of the modern discipline. Recently, I advanced a framework of analysis that, I suggested, is generally relevant for social analysis, including understanding the nature of the recent 'crisis' (Lawson 2009a). In the course of developing the arguments of the paper containing that framework, I took the opportunity to critically reference a contribution by (2008). I did so because the latter paper appeared to me to send the signal that the crisis teaches us that we need to develop different versions of the mathematical models than those hitherto used to guide policy. Although the Colander et al (2008) paper, as might be expected from such a collection of authors, is insightful, the noted response, I believe, is not the best one. Because the paper seemed to have been influential, not least in heterodox circles, I used it as a kind of foil to set out my alternative account. I was, and remain, particularly concerned that the very recent apparent rise in popularity of seemingly radical substantive theories, most especially those that are counted as Keynesian, should not be used merely to develop alternative mathematical models to those previously dominant. If my arguments about the limitations of formalism are correct, it follows that the situation of modern economics represents a very significant misallocation of resources – almost all are given over to the mathematical modelling project. Yet the seriousness of this unhappy state of affairs seems still to go largely unappreciated. So when the editor of this journal, Edward Fullbrook, invited me to produce a short paper that covered some of the same ground as in Lawson (2009a), I was happy enough to comply. However the invite was rather unusual in its details. It proposed a debate of sorts between myself and Colander et al covering those particular aspects on which we appear to disagree. Further, this debate was to take the form not of a direct engagement but of each set of contributors marshalling or summarising arguments of our earlier papers to address the statement below formulated by Fullbrook himself. This then explains the orientation of what follows. The statement in question runs as follows.
RePEc: Research Papers in Economics, 2001
RePEc: Research Papers in Economics, 1999
An investor faced with a contingent claim may eliminate risk by super hedging in a financial mark... more An investor faced with a contingent claim may eliminate risk by super hedging in a financial market As this is often quite expensive we study partial hedges which require less capital and reduce the risk In a previous paper we determined quantile hedges which succeed with maximal probability given a capital constraint Here we look for strategies which minimize the shortfall risk defined as the expectation of the shortfall weighted by some loss function The resulting efficient hedges allow the investor to interpolate in a systematic way between the extremes of no hedge and a perfect super hedge depending on the accepted level of shortfall risk.
Annual Review of Financial Economics, 2015
The quantification of downside risk in terms of capital requirements is a key issue for both regu... more The quantification of downside risk in terms of capital requirements is a key issue for both regulators and the financial industry. This review presents the axiomatic approach, which is based on monetary risk measures. These provide a unifying mathematical framework for the determination of capital requirements, for economic indices of riskiness, and for the analysis of preferences in the face of risk and Knightian uncertainty. In the special case of distribution-based risk measures, we review recent advances in characterizing their statistical properties such as elicitability and robustness.
Séminaire de Probabilités IX Université de Strasbourg, 1975
Journal of Applied Probability, 1972
We discuss the potential theory of optimal stopping for a standard process and an unbounded rewar... more We discuss the potential theory of optimal stopping for a standard process and an unbounded reward function. This is applied to Brownian motion constrained to a N(m, σ2) distribution at time 1. Boyce [2] has discovered, via computer, various interesting features of this example. We provide direct proofs for some of them, in particular for the qualitative jump of the optimal strategy as the variance σ2 passes the critical value 1.
Lecture Notes in Mathematics, 1981
Finance and Stochastics, Feb 1, 2000
Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006, Nov 9, 2009
Annals of Probability, Feb 1, 1984
Mitteilungen der Deutschen mathematiker-Vereinigung, Sep 15, 2009
Stochastic Processes and their Applications, Nov 1, 2001
Springer eBooks, Oct 10, 2005
We introduce an entropy technique which allows to treat some infinite-dimensional extensions of t... more We introduce an entropy technique which allows to treat some infinite-dimensional extensions of the classical duality equations for the time reversal of diffusion processes.
Proceedings of symposia in pure mathematics, 1977
Springer eBooks, Feb 6, 2006
Birkhäuser Basel eBooks, 1998
Richard von Mises was professor at the University of Berlin from 1920 to 1933. During these thirt... more Richard von Mises was professor at the University of Berlin from 1920 to 1933. During these thirteen years he advanced, with great vigour, the field of applied mathematics and stochastics. His research contributions cover a most impressive range, and the impact of his ideas can be felt even today.
Birkhäuser Boston eBooks, 1990
Elsevier eBooks, 1991
Abstract Stochastic integrals with respect to a martingale X often involve a predictable process ... more Abstract Stochastic integrals with respect to a martingale X often involve a predictable process integrated against the continuous martingale component Xc together with terms which are integrals of the compensated random measures associated with the jumps. The latter are related to ‘optional’ stochastic integrals. The main result of this paper relates such a stochastic integral with the sum of a predictable stochastic integral of X and an orthogonal martingale. The result has applications in the hedging of contingent claims in finance.
Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1969