We study the influence of taking liquidity costs and market impact into account when hedging a contingent claim, first in the discrete time setting, then in continuous time. In the latter case and in a complete market, we derive a fully non-linear pricing partial differential equation, and...

Within a Markovian complete financial market, we consider the problem of hedging a Bermudan option with a given probability. Using stochastic target and duality arguments, we derive a backward numerical scheme for the Fenchel transform of the pricing function. This algorithm is similar to the...

We consider the problem of option hedging in a market with proportional transaction costs. Since super-replication is very costly in such markets, we replace perfect hedging with an expected loss constraint. Asymptotic analysis for small transactions is used to obtain a tractable model. A...

Standard models for fi…nancial markets are based on the simplifying assumption that trading orders can be given and executed in continuous time with no friction. This assumption is clearly a strong idealization of the reality. In particular, securities should not be described by a single price...

We consider a class of production-investment models in discrete time with proportional transaction costs. For linear production functions, we study a natural extension of the no-arbitrage of the second kind condition introduced by M. Rasonyi [13]. We show that this condition implies the...