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 transaction costs is used to obtain a tractable model. A...

We study the problem of finding the minimal initial capital needed in order to hedge without risk a barrier option when the vector of proportions of wealth invested in each risky asset is constraint to lie in a closed convex domain. In the context of a Brownian diffusion model, we provide a PDE...

We consider a continuous time multivariate financial market with proportionaltransaction costs and study the problem of finding the minimal initialcapital needed to hedge, without risk, European-type contingent claims. Themodel is similar to the one considered in Bouchard and Touzi (2000)...