We consider a multivariate financial market with proportional transaction costs as in Kabanov (1999). We study the problem of contingent claim pricing via utility maximization as in Hodges and Neuberger (1989). Using an exponential utility function, we derive a closed form characterization for...

Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion "Samuelson" market model (also known as the Black-Scholes model because it is used in that most...

We study an optimal investment problem under contagion risk in a financial model subject to multiple jumps and defaults. The global market information is formulated as progressive enlargement of a default-free Brownian filtration, and the dependence of default times is modelled by a conditional...

We consider a multivariate financial market with transaction costs as in Kabanov. We study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. We prove that the value of this stochastic control problem is given by the cost of the...