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...

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...

We study the Leland model for hedging portfolios in the presence of a constant proportional transaction costs coefficient. The modified Leland's strategy recently defined by the second author, contrarily to the classical one, ensures the asymptotic replication of a large class of payoff. In this...

In this paper, we propose an approximation method based on Picard iterations deduced from the Doléans–Dade exponential formula. Our method allows to approximate trajectories of Markov processes in a large class, e.g. solutions to non-Lipchitz SDEs. An application to the pricing of Asian-style...

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 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...