TY  - GEN
AB  - 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* ∈ $\mathcal{Q}$  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 (ξ<sub>*t*</sub>) (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 ξ 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 $\mathcal{E}$<sup>ƒ</sup> -strong supermartingales
under *Q*, for all *Q* ∈ $\mathcal{Q}$ .
DA  - 2018
KW  - European options
KW  - American options
KW  - incomplete markets
KW  - non-linear pricing
KW  - BSDEs with constraints
KW  - constrained re ected BSDEs
KW  - ƒ-expectation
KW  - control problems with non-linear expectation
KW  - optimal stopping with non-linear expectation
KW  - non-linear optional decomposition
KW  - pricing-hedging duality
LA  - eng
PY  - 2018
SN  - 0931-6558
TI  - Superhedging prices of European and American options in a non-linear incomplete market with default
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29331479
Y2  - 2024-11-22T14:41:20
ER  -