We consider the standard discrete-time model of a frictionless financial market and show that the law of one price holds if and only if there exists a martingale density process with strictly positive initial value. In contrast to the classical no-arbitrage criteria, this density process may...

This paper investigates the relationship between the minimal Hellinger martingale measure of order q (MHM measure hereafter) and the q-optimal martingale measure for any q[not equal to]1. First, we provide more results for the MHM measure; in particular we establish its complete characterization...

This paper proposes an efficient model for the term structure of interest rates when the interest rate takes very small values. We make the following choices: (i) we model the short-term interest rate, (ii) we assume that once the interest rate reaches zero, it stays there and we have to wait...

We consider a continuous-time stochastic optimization problem with infinite horizon, linear dynamics, and cone constraints which includes as a particular case portfolio selection problems under transaction costs for models of stock and currency markets. Using an appropriate geometric formalism...

Inspired by the theory of financial markets with transaction costs, we study a concept of essential supremum in the framework where a random partial order in Rd is lifted to the space L0(Rd) of d-dimensional random variables. In contrast to the classical definition, we define the essential...