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Roxana DUMITRESCU (King’s College London) – “On E^g-pricing of American options in complete and incomplete markets with default”

April 9, 4:30 pm - 5:30 pm

1st Monday of each month

Time: 4:30 pm – 5:30 pm
Date: 09th of April 2018
Place: Room 3105

Roxana DUMITRESCU (King’s College London) – “On E^g-pricing of American options in complete and incomplete markets with default”

Abstract: We study pricing and hedging for American options in a market model with default, where there are imperfections are taken into account via the nonlinearity of the wealth dynamics. In the first part of the talk, we address the case of a complete market. We prove that  the seller’s price coincides with the value function of an optimal stopping problem with a nonlinear expectation Eg (induced by a BSDE), which corresponds to the solution of a nonlinear reflected BSDE with obstacle (ξt). Moreover, we show the existence of a superhedging portfolio strategy. We then consider the buyer’s price of the American option and show that it is equal to the value function of an optimal stopping problem with a nonlinear expectation, and that it can be characterized via the solution of a reflected BSDE with obstacle (ξt). Under the additional assumption of left upper semicontinuity along stopping times of (ξt), we show the existence of a super-hedge (τ,φ) for the buyer.

In the second part of the talk, we address the pricing and superhedging issues in the case of an incomplete market. We characterise the seller’s price as the value of a mixed optimal control/optimal stopping problem with nonlinear expectations, which is shown to admit a representation as the minimal supersolution of a nonlinear constrained reflected BSDE with lower obstacle. We then show that the buyer’s price corresponds to the value of a stochastic control/optimal stopping game with E^g-expectations, which is related to the maximal sub solution of a constrained reflected BSDE with lower obstacle. We moreover show that under appropriate conditions the game admits a value.  We emphasise the fact that we are able to derive a dynamic representation of the buyer’s price, our approach being based on recent results obtained in the paper “BSDEs with weak reflections and partial hedging of American options”.

 

 

Details

Date:
April 9
Time:
4:30 pm - 5:30 pm
Event Categories:
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Organizers

Caroline HILLAIRET
Peter TANKOV