We study super-replication of contingent claims in markets with delay. This can be viewed as a stochastic target problem with delayed filtration. First, we establish a duality result for this setup . Our second result says that the scaling limit of super--replication prices for binomial models with a fixed number moments of delay is equal to the G--expectation with volatility uncertainty interval which we compute explicitly .
We study super-replication of contingent claims in markets with delayed filtration. The first result in this paper reveals that in the Black--Scholes model with constant delay the super-replication price is prohibitively costly and leads to trivial buy-and-hold strategies . Our second result says that the scaling limit of super--replication prices for binomial models with a fixed number of times of delay H is equal to the G--expectation with volatility uncertainty interval 0,\sigma\sqrt{H+1 .
D
delay. This can be viewed as a stochastic target problem with
R
First, we establish a duality result for this setup
The first result in this paper reveals that in the Black--Scholes model with constant delay the super-replication price is prohibitively costly and leads to trivial buy-and-hold strategies
R
moments of delay
of times of delay H
R
which we compute explicitly
0,\sigma\sqrt{H+1