919 research outputs found
Duality and convergence for binomial markets with friction
We prove limit theorems for the super-replication cost of European options in a binomial model with friction. Examples covered are markets with proportional transaction costs and illiquid markets. A dual representation for the super-replication cost in these models is obtained and used to prove the limit theorems. In particular, the existence of a liquidity premium for the continuous-time limit of the model proposed in Çetin etal. (Finance Stoch. 8:311-341, 2004) is proved. Hence, this paper extends the previous convergence result of Gökay and Soner (Math Finance 22:250-276, 2012) to the general non-Markovian case. Moreover, the special case of small transaction costs yields, in the continuous limit, the G-expectation of Peng as earlier proved by Kusuoka (Ann. Appl. Probab. 5:198-221, 1995
Super-replication with nonlinear transaction costs and volatility uncertainty
We study super-replication of contingent claims in an illiquid market with
model uncertainty. Illiquidity is captured by nonlinear transaction costs in
discrete time and model uncertainty arises as our only assumption on stock
price returns is that they are in a range specified by fixed volatility bounds.
We provide a dual characterization of super-replication prices as a supremum of
penalized expectations for the contingent claim's payoff. We also describe the
scaling limit of this dual representation when the number of trading periods
increases to infinity. Hence, this paper complements the results in [11] and
[19] for the case of model uncertainty
Robust Hedging with Proportional Transaction Costs
Duality for robust hedging with proportional transaction costs of path
dependent European options is obtained in a discrete time financial market with
one risky asset. Investor's portfolio consists of a dynamically traded stock
and a static position in vanilla options which can be exercised at maturity.
Both the stock and the option trading is subject to proportional transaction
costs. The main theorem is duality between hedging and a Monge-Kantorovich type
optimization problem. In this dual transport problem the optimization is over
all the probability measures which satisfy an approximate martingale condition
related to consistent price systems in addition to the usual marginal
constraints
Hedging, arbitrage and optimality with superlinear frictions
In a continuous-time model with multiple assets described by c\`{a}dl\`{a}g
processes, this paper characterizes superhedging prices, absence of arbitrage,
and utility maximizing strategies, under general frictions that make execution
prices arbitrarily unfavorable for high trading intensity. Such frictions
induce a duality between feasible trading strategies and shadow execution
prices with a martingale measure. Utility maximizing strategies exist even if
arbitrage is present, because it is not scalable at will.Comment: Published at http://dx.doi.org/10.1214/14-AAP1043 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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