The post-crisis financial reforms address the need for systemic regulation, focused not only on individual banks but also on the whole financial system. The regulator principal objective is to set banks' capital requirements equal to international minimum standards in order to mimimise systemic...

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...

This paper proves the Fundamental Theorem of Asset Pricing with transaction costs, when bid and ask prices follow locally bounded cadlag (right-continuous, left-limited) processes. The Robust No Free Lunch with Vanishing Risk (RNFLVR) condition for simple strategies is equivalent to the...

We study the Leland model for hedging portfolios in the presence of a constant proportional transaction costs coefficient. The modi fied Leland's strategy defi ned in [2], contrarily to the classical one, ensures the asymptotic replication of a large class of payoff . In this setting, we prove a...

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...

In frictionless markets, the absence of arbitrage opportunities is equivalent to the existence of a martingale process evolving in the ray R_ S where S is the d-dimensional price process (whose first component is the numeraire). With transaction costs, absence of arbitrage opportunities is...

We consider two quasi-linear initial-value Cauchy problems on Rd: a parabolic system and an hyperbolic one. They both have a first order non-linearity of the form φ(t, x, u) · ∇u, a forcing term h(t, x, u) and an initial condition u0 ∈ L∞ (Rd ) ∩ C ∞ (Rd ), where φ (resp. h) is...

In contrast with the classical models of frictionless financial markets, market models with proportional transaction costs, even satisfying usual no-arbitrage properties, may admit arbitrage opportunities of the second kind. This means that there are self-financing portfolios with initial...

We study the Leland model for hedging portfolios in the presence of a constant proportional transaction costs coefficient. The modified Leland's strategy defined in [2], contrarily to the classical one, ensures the asymptotic replication of a large class of payoff. In this setting, we prove a...

In 1985 Leland suggested an approach to price contingent claims under proportional transaction costs. Its main idea is to use the classical Black–Scholes formula with a suitably adjusted volatility for a periodical revision of the portfolio whose terminal value approximates the pay-off....