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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

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

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

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

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

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

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

Measure theory Halmos, Paul R. | Van Nostrand Reinhold Co. 1969 Nouveau

Stochastic optimal controlthe discrete time case Bertsekas, Dimitri P. | Academic Press 1978 Nouveau

Lebesgue integration Williamson, J. H. | Holt Rinehart and Winston 1962 Nouveau

Vector measures Dinculeanu, N. | Veb Deutscher Verlag Der Wissenschaften 1966 Nouveau

The Lebesgue integral Burkill, J. C. | Cambridge University Press 1971 Nouveau

Leçons sur les ensembles analytiques et leurs applications Lusin, Nicolas ; Lebesgue, Henri ; Sierpinski, M. | Gauthier-Villars et Cie. 1930 Nouveau

Vector measures Dinculeanu, N. | Pergamon Press;Veb Deutscher Verlag Der Wissenschaften 1967 Nouveau

Intégrales de Lebesgue Fonctions d'ensemble Classes de Baire De La Vallée Poussin, C. | Gauthier-Villars 1916 Nouveau

The structure of Lebesgue integration theory Temple, G. | Oxford at the Clarendon Press 1971 Nouveau

Capacités et processus stochastiques Dellacherie, Claude | Springer 1972 Nouveau

Conjuntos ordenados y ramificados Ricabarra, Rodolfo A. | Instituto de matematica Universidad nacional del Sur 1958 Nouveau

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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

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

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

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

Stochastic optimal control
the discrete time case Bertsekas, Dimitri P. | Academic Press 1978 Nouveau