2,608 research outputs found
Variance optimal hedging for continuous time additive processes and applications
For a large class of vanilla contingent claims, we establish an explicit
F\"ollmer-Schweizer decomposition when the underlying is an exponential of an
additive process. This allows to provide an efficient algorithm for solving the
mean variance hedging problem. Applications to models derived from the
electricity market are performed
Optimal Skorokhod embedding under finitely-many marginal constraints
The Skorokhod embedding problem aims to represent a given probability measure
on the real line as the distribution of Brownian motion stopped at a chosen
stopping time. In this paper, we consider an extension of the optimal Skorokhod
embedding problem to the case of finitely-many marginal constraints. Using the
classical convex duality approach together with the optimal stopping theory, we
obtain the duality results which are formulated by means of probability
measures on an enlarged space. We also relate these results to the problem of
martingale optimal transport under multiple marginal constraints
Duality for pathwise superhedging in continuous time
We provide a model-free pricing-hedging duality in continuous time. For a
frictionless market consisting of risky assets with continuous price
trajectories, we show that the purely analytic problem of finding the minimal
superhedging price of a path dependent European option has the same value as
the purely probabilistic problem of finding the supremum of the expectations of
the option over all martingale measures. The superhedging problem is formulated
with simple trading strategies, the claim is the limit inferior of continuous
functions, which allows for upper and lower semi-continuous claims, and
superhedging is required in the pathwise sense on a -compact sample
space of price trajectories. If the sample space is stable under stopping, the
probabilistic problem reduces to finding the supremum over all martingale
measures with compact support. As an application of the general results we
deduce dualities for Vovk's outer measure and semi-static superhedging with
finitely many securities
Pathwise super-replication via Vovk's outer measure
Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback
option. In: Finance Stoch. (1998)] the connection between model-independent
pricing and the Skorokhod embedding problem has been a driving force in robust
finance. We establish a general pricing-hedging duality for financial
derivatives which are susceptible to the Skorokhod approach.
Using Vovk's approach to mathematical finance we derive a model-independent
super-replication theorem in continuous time, given information on finitely
many marginals. Our result covers a broad range of exotic derivatives,
including lookback options, discretely monitored Asian options, and options on
realized variance.Comment: 18 page
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