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Research talks;Analysis and its Applications;Computer Science;Control Theory and Optimization;Mathematics in Science and Technology;Probability and Statistics

I discuss some recent developments related to the robust framework for pricing and hedging in discrete time. I introduce pointwise approach based on pathspace restrictions and compare it with the quasi-sure setting of Bouchard and Nutz (2015), and show that their versions of the Fundamental Theorem of Asset Pricing and the Pricing-Hedging duality may be deduced one from the other via a construction of a suitable set of paths which represents a given set of measures. I show that the setup with statically traded hedging instruments can be naturally lifted to a setup with only dynamically traded assets without changing the superhedging prices. This allows one to deduce, in particular, a pricing-hedging duality for American options. Subsequently, I focus on the superhedging problem and discuss the choice of a trading strategy amongst all feasible super-hedging strategies. First, I establish existence of a minimal superhedging strategy and characterise its value via a concave envelope construction. Then I introduce a secondary problem of maximisation of expected utility of consumption. Building on Nutz (2014) and Blanchard and Carassus (2017) I provide suitable assumptions under which an optimal strategy exists and is unique. Finally, I also explain how additional information can be seen as a further restriction of the pathspace. This allows one to quantify to value of such a new information. The talk is based on a number of recent works (see references) as well as ongoing research with Johannes Wiesel. I discuss some recent developments related to the robust framework for pricing and hedging in discrete time. I introduce pointwise approach based on pathspace restrictions and compare it with the quasi-sure setting of Bouchard and Nutz (2015), and show that their versions of the Fundamental Theorem of Asset Pricing and the Pricing-Hedging duality may be deduced one from the other via a construction of a suitable set of paths which represents a ...

91G20 ; 91B70 ; 60G40 ; 60G42 ; 90C46 ; 90C47 ; 28A05 ; 49N15

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Documents 60G40 | enregistrements trouvés : 33

Pathwise or quasi-sure towards dynamic robust framework for pricing and hedging Obloj, Jan | CIRM H Nouveau

Théorie du potentiel :proceedings of the colloque Jacques Deny held at orsay#June 20-23 Mokobodzki, G. ; Pinchon, D. | Springer-Verlag 1984 Nouveau

Filtering and control of random processesproceedings of the e.n.s.t.,c.n.e.t.,colloquium held in paris,france,feb. 23-24,1983 Korezlioglu, H. ; Mazziotto, G. ; Szpirglas, J. | Springer-Verlag 1984 Nouveau

Séminaire de probability IIIUniversité de StrasbourgOct. 1967 - Juin 1968 | Springer-Verlag 1969 Nouveau

Martingalesa report on a meeting at OberwolfachMay 17-23 Dinges, Hermann | Springer-Verlag 1971 Nouveau

Probabilistic methods in differential equationsproceedings of the conference held at the University of Victoria, British ColumbiaAug. 19-20 Pinsky, M. A. | Springer-Verlag 1975 Nouveau

Séminaire de probabilités VII | Springer-Verlag 1973 Nouveau

Mathematics of finance :proceedings of an AMS-IMS-SIAM joint summer research conference on ...#June 22-26 Yin, G. George ; Zhang, Qing | American Mathematical Society 2004 Nouveau

Actas del cuarto congreso Dr. Antonio A. R. Monteiro Departemento de Matematica | Departamento de Matematica ( UNS );Instituto de Matematica ( CONICET ) 1997 Nouveau

Orthogonal families and semigroups in analysis and probability Graczyk, Piotr ; Urbina, Wilfredo | Société Mathématique de France 2012 Nouveau

Arbitrages in a progressive enlargement of filtration Jeanblanc, Monique | CIRM Nouveau

Optimal stopping rules Shiryayev, A. N. | Springer-Verlag 1978 Nouveau

Probability methods for approximations in stochastic control and for elliptic equations Kushner, Harold J. | Academic Press 1977 Nouveau

Amarts and set function processes Gut, Allan ; Schmidt, Klaus D. | Springer-Verlag 1983 Nouveau

Inequalities for stopped brownian motion Van Der Vecht, D. P. | Centre For Mathematics And Computer Science 1986 Nouveau

Stochastic differential equations :an introduction with applications Oksendal, Bernt | Springer-Verlag 1985 Nouveau

Stopping times and dirested processes Edgar, G. A. ; Sucheston, Louis | Cambridge University Press 1992 Nouveau

Stochastic differential equations :an introduction with applications Oksendal, Bernt | Springer 1988 Nouveau

Probability theory III :stochastic calculus Prokhorov, Yu. V. ; Shiryaev, A. N. | Springer 1998 Nouveau

Decoupling :From dependence to independence randomly stopped processes u-statistics and processes martingales and beyond De la pena, Victor h. ; Gine, Evarist | Springer 1999 Nouveau

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Théorie du potentiel :
proceedings of the colloque Jacques Deny held at orsay#June 20-23 Mokobodzki, G. ; Pinchon, D. | Springer-Verlag 1984 Nouveau

Filtering and control of random processes
proceedings of the e.n.s.t.,c.n.e.t.,colloquium held in paris,france,feb. 23-24,1983 Korezlioglu, H. ; Mazziotto, G. ; Szpirglas, J. | Springer-Verlag 1984 Nouveau

Séminaire de probability III
Université de Strasbourg
Oct. 1967 - Juin 1968 | Springer-Verlag 1969 Nouveau

Martingales
a report on a meeting at Oberwolfach
May 17-23 Dinges, Hermann | Springer-Verlag 1971 Nouveau

Probabilistic methods in differential equations
proceedings of the conference held at the University of Victoria, British Columbia
Aug. 19-20 Pinsky, M. A. | Springer-Verlag 1975 Nouveau

Mathematics of finance :
proceedings of an AMS-IMS-SIAM joint summer research conference on ...#June 22-26 Yin, G. George ; Zhang, Qing | American Mathematical Society 2004 Nouveau

Stochastic differential equations :
an introduction with applications Oksendal, Bernt | Springer-Verlag 1985 Nouveau

Stochastic differential equations :
an introduction with applications Oksendal, Bernt | Springer 1988 Nouveau

Probability theory III :
stochastic calculus Prokhorov, Yu. V. ; Shiryaev, A. N. | Springer 1998 Nouveau

Decoupling :
From dependence to independence
randomly stopped processes u-statistics and processes martingales and beyond De la pena, Victor h. ; Gine, Evarist | Springer 1999 Nouveau