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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 28A05 | enregistrements trouvés : 53

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

Group representations, ergodic theory, and mathematical physics :a tribute to George W. MackeyAMS special session honoring the memory of George W. Mackey#Jan. 7-8 Doran, Robert S. ; Moore, Calvin C. ; Zimmer, Robert J. | Amercian Mathematical Society 2008 Nouveau

Séminaire Bourbaki. Vol. 1983/84 :exposés 615-632 | Société Mathématique de France 1985 Nouveau

Séminaire de probabilités XI Dellacherie , C. ; Meyer, P. A. ; Weil, M. | Springer-Verlag 1977 Nouveau

Séminaire de probabilités X. Université Meyer, P. A. | Springer-Verlag 1976 Nouveau

Measure and measurable dynamics :conference on...,in honor of Dorothy Maharam stone, held at the university of Rochester#Sept. 17- 19 Mauldin, R. Daniel ; Shortt, R. M. ; Silva, Cesar E. | American Mathematical Society 1989 Nouveau

The calculus of non-measurable functions and sets Andersen, N. T. | Mathematics Institute University 1985 Nouveau

Construction of Borel measures on metric spaces Kornum, Peer | Aarhus Universitet Matematisk Institut 1980 Nouveau

Analytic setsdeveloped from lectures given at the London Mathematical Society instructional conference on... held at the University College London, july 16-29, 1978 Rogers, C. A. ; Jayne, J. E. ; Dellacherie , C. | Academic Press 1980 Nouveau

Measure and integration Salamon, Dietmar A. | European Mathematical Society 2016 Nouveau

Foundations of abstract analysis Dshalalow, Jewgeni H. | Springer 2013 Nouveau

Selected topics in combinatorial analysis Kurilic, Milos ; Todorcevic, Stevo | Matematicki Institut SANU 2015 Nouveau

Measure theory Cohn, Donald L. | Birkhäuser 2013 Nouveau

Potential wadge classes Lecomte, Dominique | American Mathematical Society 2012 Nouveau

The structure of the real line Bukovsky, Lev | Birkhäuser 2011 Nouveau

Integral geometry and Radon transforms Helgason, Sigurdur | Springer 2010 Nouveau

Analysis III Amann, Herbert ; Escher, Joachim ; Levy, Silvio ; Cargo, Matthew | Birkhäuser 2009 Nouveau

Descriptive set theory Moschovakis, Yiannis N. | American Mathematical Society 2009 Nouveau

Geometric integration theory Krantz, Steven G. ; Parks, Harold R. | Birkhäuser 2008 Nouveau

Invitation to ergodic theory Silva, C. E. | Amercian Mathematical Society 2008 Nouveau

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Group representations, ergodic theory, and mathematical physics :
a tribute to George W. Mackey
AMS special session honoring the memory of George W. Mackey#Jan. 7-8 Doran, Robert S. ; Moore, Calvin C. ; Zimmer, Robert J. | Amercian Mathematical Society 2008 Nouveau

Séminaire Bourbaki. Vol. 1983/84 :
exposés 615-632 | Société Mathématique de France 1985 Nouveau

Measure and measurable dynamics :
conference on...,in honor of Dorothy Maharam stone, held at the university of Rochester#Sept. 17- 19 Mauldin, R. Daniel ; Shortt, R. M. ; Silva, Cesar E. | American Mathematical Society 1989 Nouveau

Analytic sets
developed from lectures given at the London Mathematical Society instructional conference on... held at the University College London, july 16-29, 1978 Rogers, C. A. ; Jayne, J. E. ; Dellacherie , C. | Academic Press 1980 Nouveau