Hans Foellmer

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University of Helsinki

Luciano Campi

London School of Economics and Political Science

Monique Jeanblanc

Evry University

Hans Föllmer

Marek Rutkowski

The University of Sydney

Libo Li

Hardy Hulley

University of Technology Sydney

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Papers by Hans Foellmer

Anticipation cancelled by a Girsanov transformation : a paradox on Wiener space

Annales De L Institut Henri Poincare-probabilites Et Statistiques, 1993

L'accès aux archives de la revue « Annales de l'I. H. P., section B » () implique l'accord avec l... more L'accès aux archives de la revue « Annales de l'I. H. P., section B » () implique l'accord avec les conditions générales d'utilisation (). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques

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Optional decomposition and Lagrange multipliers

Finance and Stochastics, Nov 1, 1997

Let Q be the set of equivalent martingale measures for a given process S, and let X be a process ... more Let Q be the set of equivalent martingale measures for a given process S, and let X be a process which is a local supermartingale with respect to any measure in Q. The optional decomposition theorem for X states that there exists a predictable integrand ϕ such that the difference Xϕ • S is a decreasing process. In this paper we give a new proof which uses techniques from stochastic calculus rather than functional analysis, and which removes any boundedness assumption.

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Probabilistic Aspects of Financial Risk

Birkhäuser Basel eBooks, 2001

Ux y ( H qv U g ' q ( ed fy i x f g h g j i i q lk m nx o v p t fx qq r is t u d vx w f i vk p x ... more Ux y ( H qv U g ' q ( ed fy i x f g h g j i i q lk m nx o v p t fx qq r is t u d vx w f i vk p x zy lk Ux u p gk n |{ x q } ~ n t u n o n $ nx f |v U i t i lk $ v g ek Uo t u i i ¤w v g k n to qv x nx f Ht u tx fw x v n j k U x v t v U w v n g i vk p k U x v gk n x v U ( Ts b p h qv U fx qk U d qk n it y ~} w v Ux y ( rx qq it (t u v U d qk n d i b t x qq lk n iv gk U fw x v p q tx v no fw uk n x ' p x t v

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Hedging by Sequential Regression: an Introduction to the Mathematics of Option Trading

Astin Bulletin, Nov 1, 1989

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Monetary Valuation of Cash Flows Under Knightian Uncertainty

International Journal of Theoretical and Applied Finance, Feb 1, 2011

The classical valuation of an uncertain cash flow in discrete time consists in taking the expecta... more The classical valuation of an uncertain cash flow in discrete time consists in taking the expectation of the sum of the discounted future payoffs under a fixed probability measure, which is assumed to be known. Here we discuss the valuation problem in the context of Knightian uncertainty. Using results from the theory of convex risk measures, but without assuming the existence of a global reference measure, we derive a robust representation of concave valuations with an infinite time horizon, which specifies the interplay between model uncertainty and uncertainty about the time value of money.

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Random economies with many interacting agents

Journal of Mathematical Economics, Mar 1, 1974

... Note that these files are not on the IDEAS site. Please be patient as the files may be large.... more ... Note that these files are not on the IDEAS site. Please be patient as the files may be large. ... [Downloadable!] (restricted) Other versions: William A. Brock & Steven N. Durlauf, 1995. "Discrete Choice with Social Interactions I: Theory," Working Papers 95-10-084, Santa Fe Institute. ...

Optional decompositions under constraints

RePEc: Research Papers in Economics, 1997

Motivated by a hedging problem in mathematical nance, El Karoui and Quenez 7] and Kramkov 1 4 ] h... more Motivated by a hedging problem in mathematical nance, El Karoui and Quenez 7] and Kramkov 1 4 ] h a ve d e v eloped optional versions of the Doob-Meyer decomposition which hold simultaneously for all equivalent martingale measures. We i n vestigate the general structure of such optional decompositions, both in additive and in multiplicative form, and under constraints corresponding to di erent classes of equivalent measures. As an application, we extend results of Karatzas and Cvitani c 3] on hedging problems with constrained portfolios.

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Risk assessment for uncertain cash flows: Model ambiguity, discounting ambiguity, and the role of bubbles

arXiv (Cornell University), Feb 19, 2010

We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for... more We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for processes as introduced in Cheridito, Delbaen, and Kupper [11]. These risk measures take into account not only the amounts but also the timing of a cash flow. We discuss their robust representation in terms of suitably penalized probability measures on the optional σ-field. This yields an explicit analysis both of model and discounting ambiguity. We focus on supermartingale criteria for different notions of time consistency. In particular we show how "bubbles" may appear in the dynamic penalization, and how they cause a breakdown of asymptotic safety of the risk assessment procedure.

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9 Hedging under constraints

De Gruyter eBooks, Mar 11, 2013

Chapter 7. Superhedging

De Gruyter eBooks, Aug 9, 2002

Chapter 3. Optimality and equilibrium

De Gruyter eBooks, Aug 9, 2002

Convex measures of risk and trading constraints

RePEc: Research Papers in Economics, 2001

We shall study the paper (3) by H.Follmer and A. Schied. Here the authors introduce the notion of... more We shall study the paper (3) by H.Follmer and A. Schied. Here 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 they prove a corresponding extension of the representation theorem in terms of probability measures on the underlying space of scenarios. As a case study, they 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.

6 American contingent claims

De Gruyter eBooks, Mar 11, 2013

Chapter 2. Preferences

De Gruyter eBooks, Aug 9, 2002

Chapter 5. Dynamic arbitrage theory

De Gruyter eBooks, Aug 9, 2002

Chapter 4. Monetary measures of risk

De Gruyter eBooks, Aug 9, 2002

Chapter 6. American contingent claims

De Gruyter studies in mathematics, Aug 9, 2002

Chapter 8. Efficient hedging

De Gruyter eBooks, Aug 9, 2002

4 Monetary measures of risk

De Gruyter eBooks, Mar 11, 2013

A Probabilistic Look at Options and at the Underlying Randomness

Consider an option based on a financial asset whose price fluctuation is modelled by a stochastic... more Consider an option based on a financial asset whose price fluctuation is modelled by a stochastic process (St) over some probability space (Ω, F, P). Let H denote the resulting pay-off; for a call option with exercise price c and terminal time T we would have H = (S t - c)+. Instead of computing the fair price of such an option as the expected value E[H] with respect to P, possibly modified by a risk premium, the Black-Scholes formula computes the price as the expected value E* [H] with respect to a new measure P* which turns (S t ) into a martingale. We review the basic argument, both froma probabilistic and an economic point of view. It involves the Ito representation of H as a stochastic integral of the price process and the interpretation of the integrand as a dynamical hedging strategy. Such hedging strategies induce a technical demand for the financial asset. Thus the question arises: What is the impact of such strategies on the underlying price process?

Anticipation cancelled by a Girsanov transformation : a paradox on Wiener space

Annales De L Institut Henri Poincare-probabilites Et Statistiques, 1993

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Optional decomposition and Lagrange multipliers

Finance and Stochastics, Nov 1, 1997

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Probabilistic Aspects of Financial Risk

Birkhäuser Basel eBooks, 2001

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Hedging by Sequential Regression: an Introduction to the Mathematics of Option Trading

Astin Bulletin, Nov 1, 1989

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