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...

We consider a consumption-investment optimization problem for the Kabanov model when the proportional transaction costs rate is constant and the prices are modeled by a Lévy process. We naturally extend the preliminary work of [4] to portfolio processes that are only supposed to be làdlàg....

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...

Local volatility models are popular because they can be simply calibrated to the market of European options. For such models, we propose a modified Leland method which allows us to approximately replicate a European contingent claim when the market is under proportional transaction costs. The...