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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 60G42 | enregistrements trouvés : 42

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

Probability and analysislectures given at the 1st 1985 session of the centro internazionale matematico estivo,c.i.m.e, held at varenna como,italy may 31-june 8,1985 Letta, G. ; Pratelli, M. | Springer-Verlag 1986 Nouveau

Séminaire de probabilités 1967-1980 :a selection in martingale theory Emery, Michel ; Yor, Marc | Springer 2002 Nouveau

Séminaire Bourbaki. Vol. 2000/2001 :exposés 880-893 | Société Mathématique de France 1998 Nouveau

Pricing without martingale measure Carassus, Laurence | CIRM H Nouveau

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

Two-parameter martingales and their quadratic variation Imkeller, Peter | Springer-Verlag 1988 Nouveau

Discrete-parameter martingales Neveu, J. | North-Holland Publishing Co. 1975 Nouveau

Advances in probability and related topics. Vol. 3 Ney, Peter d. ; Port, Sidney | Marcel Dekker, Inc. 1974 Nouveau

Martingale Hardy spaces and their applications in Fourier analysis Weisz, Ferenc | Springer-Verlag 1994 Nouveau

Processus aléatoires gaussiens Ibrahimov, I. ; Rozanov, Y. ; Sokova, A. | Editions Mir 1974 Nouveau

Denumerable Markov chains Kemeny, John G. ; Snell, J. Laurie ; Knapp, Anthony W. | D. Van Nostrand Co. Inc. 1966 Nouveau

Probability theory, an analytic view Stroock, Daniel W. | Cambridge University Press 1993 Nouveau

Stochastic processes and the Wiener integral Yeh, J. | Marcel Dekker 1973 Nouveau

Random iterative models Duflo, Marie | Springer-Verlag 1997 Nouveau

Theory of martingales Liptser, R. Sh. ; Shiryayev, A. N. | Kluwer Academic Publishers 1986 Nouveau

Probability theoryindependence, interchangeability, martingales Chow, Yuan Shih ; Teicher, Henry | Springer 1997 Nouveau

Essentials of stochastic processes Durrett, Rick | Springer 1999 Nouveau

Probability essentials Jacod, Jean ; Protter, Philip | Springer 2000 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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Probability and analysis
lectures given at the 1st 1985 session of the centro internazionale matematico estivo,c.i.m.e, held at varenna como,italy may 31-june 8,1985 Letta, G. ; Pratelli, M. | Springer-Verlag 1986 Nouveau

Séminaire de probabilités 1967-1980 :
a selection in martingale theory Emery, Michel ; Yor, Marc | Springer 2002 Nouveau

Séminaire Bourbaki. Vol. 2000/2001 :
exposés 880-893 | Société Mathématique de France 1998 Nouveau

Probability theory
independence, interchangeability, martingales Chow, Yuan Shih ; Teicher, Henry | Springer 1997 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