Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/201632 
Year of Publication: 
2018
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 607
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Abstract: 
This paper studies the superhedging prices and the associated superhedging strategies for European and American options in a non-linear incomplete market with default. We present the seller's and the buyer's point of view. The underlying market model consists of a risk-free asset and a risky asset driven by a Brownian motion and a compensated default martingale. The portfolio process follows non-linear dynamics with a non-linear driver ƒ. By using a dynamic programming approach, we first provide a dual formulation of the seller's (superhedging) price for the European option as the supremum over a suitable set of equivalent probability measures Q ϵ Q of the ƒ-evaluation/expectation under Q of the payoff. We also provide an infinitesimal characterization of this price as the minimal supersolution of a constrained BSDE with default. By a form of symmetry, we derive corresponding results for the buyer. We also give a dual representation of the seller's (superhedging) price for the American option associated with an irregular payoff (ϵt) (not necessarily càdlàg) in terms of the value of a non-linear mixed control/stopping problem. We also provide an infinitesimal characterization of this price in terms of a constrained reflected BSDE. When ϵ is càdlàg, we show a duality result for the buyer's price. These results rely on first establishing a non-linear optional decomposition for processes which are ϵf -strong supermartingales under Q, for all Q ϵ Q.
Subjects: 
European options
American options
incomplete markets
non-linear pricing
BSDEs with constraints
constrained reflected BSDEs
f-expectation
control problems with non-linear expectation
optimal stopping with non-linear expectation
non-linear optional decomposition
pricing-hedging duality
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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