Bregman and Clay recently characterized which right-angled Artin groups with geometric dimension 2 have vanishing minimal volume entropy. In this note, we extend characterization to higher dimensions.

We apply the quadratic hedging scheme developed by Föllmer, Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process. The main contributions of this work consist of showing that local risk-minimizing strategies with respect to the physical measure do exist, even though an associated minimal martingale measure is only available in the pres...

In this paper we consider minimax games for stochastic uncertain systems with the pay-off being a nonlinear functional of the uncertain measure where the uncertainty is measured in terms of relative entropy between the uncertain and the nominal measure. The maximizing player is the uncertain measure, while the minimizer is the control which induces a nominal measure. Existence and uniqueness of...

The minimal distance equivalent martingale measure (EMM) defined in Goll and Rüschendorf (2001) is the arbitrage-free equilibrium pricing measure. This paper provides an algorithm to approximate its density and the fair price of any contingent claim in an incomplete market. We first approximate the infinite dimensional space of all EMMs by a finite dimensional manifold of EMMs. A Riemannian geo...

We define and investigate the notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme conditions and the entropy exchange computed with respect to any initial state supported on the code. In general the entropy of a code can be viewed as a ...

We characterize those vector-valued stochastic processes (with a finite index set and defined on an arbitrary stochastic base) which can become a martingale under an equivalent change of measure. This solves a problem which arises in the study of finite period securities markets with one riskless bond and a finite number of risky stocks. In this setting, our characterization provides necessary ...

In this paper, we are interested in the one-dimensional porous medium equation when the initial condition is the distribution function of a probability measure. We associate a nonlinear martingale problem with it. After proving uniqueness for the martingale problem, we show existence owing to a propagation of chaos result for a system of weakly interacting di usion processes. The particle syste...