We show how optimal Hankel-norm approximations of dynamical systems allow for a straightforward interpretation in terms of system trajectories. It is shown that for discrete time single-input systems optimal reductions are obtained by cutting 'balanced trajectories', i.e., by disconnecting the...

We investigate the problem of optimal state reduction under minimization of the angle between system behaviors. The angle is defined in a worst-case sense, as the largest angle that can occur between a system trajectory and its optimal approximation in the reduced order model. This problem is...

A bank's liquidity risk lays in the intersection of funding risk and market liquidity risk. We offer a mathematical framework to make Economic Capital and RAROC sensitive to illiquidity. We introduce the concept of a liquidity cost profile as a quantification of a bank's illiquidity at balance...

We present attractiveness, a refinement criterion for evolutionary equilibria. Equilibria surviving this criterion are robust to small perturbations of the underlying payoff system or the dynamics at hand. Furthermore, certain attractive equilibria are equivalent to others for certain...

We introduce a new kind of projection dynamics by employing a ray-projection both locally and globally. By global (local) we mean a projection of a vector (close to the unit simplex) unto the unit simplex along a ray through the origin. Using a correspondence between local and global...

We introduce and analyze expected balanced uncertain utility (EBUU) theory. A prior and a balanced outcome-set utility characterize an EBUU decision maker. Conditional on a reference or "balancing value," the latter assigns a utility to each outcome-set. The decision maker associates with each...