We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for large financial markets with small proportional transaction costs $\la_n$ on market $n$ in terms of contiguity properties of sequences of equivalent probability measures induced...

We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for a sequence of financial markets with small proportional transaction costs in terms of contiguity properties of sequences of equivalent probability measures induced by consistent...

In the modern version of Arbitrage Pricing Theory suggested by Kabanov and Kramkov the fundamental fi nancially meaningful concept is an asymptotic arbitrage. The 'real world' large market is represented by a sequence of 'models' and, though each of them is arbitrage free, investors may obtain...

We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for a sequence of financial markets with small proportional transaction costs λ n on market n, in terms of contiguity properties of sequences of equivalent probability measures...

This thesis deals with different problems related to markets with transaction costs and is composed of four parts.In part I, we begin with the study of assymptotic hedging a European option in a local volatility model with bid-ask spread.In part II, we study the optimal consumption problem in a...

We propose a continuous time model for financial markets with proportional transactions costs and a continuum of risky assets. This is motivated by bond markets in which the continuum of assets corresponds to the continuum of possible maturities. Our framework is well adapted to the study of...

We consider a fractional version of the Heston model where the two standard Brownian motions are replaced by two fractional Brownian motions with Hurst parameter H ∈ (1/2, 1). We show that the stochastic differential equation admits a unique positive solution by adapting and generalizing some...