Convex Duality with Transaction Costs

Convex Duality with Transaction Costs

Copyright: © 2016 INFORMS Abstract. Convex duality for two different super-replication problems in a continuous time financial market with proportional transaction cost is proved. In this market, static hedging in a finite number of options, in addition to usual dynamic hedging with the underlying stock, are allowed. The first one of the problems considered is the modelindependent hedging that ...

Hedging of Claims with Physical Delivery under Convex Transaction Costs

We study superhedging of contingent claims with physical delivery in a discretetime market model with convex transaction costs. Our model extends Kabanov’s currency market model by allowing for nonlinear illiquidity effects. We show that an appropriate generalization of Schachermayer’s robust no arbitrage condition implies that the set of claims hedgeable with zero cost is closed in probability...

Duality Theory for Portfolio Optimisation under Transaction Costs

For portfolio optimisation under proportional transaction costs, we provide a duality theory for general càdlàg price processes. In this setting, we prove the existence of a dual optimiser as well as a shadow price process in a generalised sense. This shadow price is defined via a “sandwiched” process consisting of a predictable and an optional strong supermartingale and pertains to all strateg...

Futures trading with transaction costs

A model for optimal consumption and investment is posed whose solution is provided by the classical Merton analysis when there is zero transaction cost. A probabilistic argument is developed to identify the loss in value when a proportional transaction cost is introduced. There are two sources of this loss. The first is a loss due to “displacement” that arises because one cannot maintain the op...

Option Hedging with Transaction Costs