Execution and block trade pricing with optimal constant rate of participation

When executing their orders, investors are proposed different strategies by brokers and investment banks. Most orders are executed using VWAP algorithms. Other basic execution strategies include POV (also called PVol) -- for percentage of volume --, IS -- implementation shortfall -- or Target Close. In this article dedicated to POV strategies, we develop a liquidation model in which a trader is constrained to liquidate a portfolio with a constant participation rate to the market. Considering the functional forms commonly used by practitioners for market impact functions, we obtain a closed-form expression for the optimal participation rate. Also, we develop a microfounded risk-liquidity premium that permits to better assess the costs and risks of execution processes and to give a price to a large block of shares. We also provide a thorough comparison between IS strategies and POV strategies in terms of risk-liquidity premium

Neumark Operators and Sharp Reconstructions, the finite dimensional case

A commutative POV measure $F$ with real spectrum is characterized by the existence of a PV measure $E$ (the sharp reconstruction of $F$) with real spectrum such that $F$ can be interpreted as a randomization of $E$. This paper focuses on the relationships between this characterization of commutative POV measures and Neumark's extension theorem. In particular, we show that in the finite dimensional case there exists a relation between the Neumark operator corresponding to the extension of $F$ and the sharp reconstruction of $F$. The relevance of this result to the theory of non-ideal quantum measurement and to the definition of unsharpness is analyzed.Comment: 37 page

POV: Obama's ban on juvenile solitary confinement

Point of view article in BU Toda

Localization of Events in Space-Time

The present paper deals with the quantum coordinates of an event in space-time, individuated by a quantum object. It is known that these observables cannot be described by self-adjoint operators or by the corresponding spectral projection-valued measure. We describe them by means of a positive-operator-valued (POV) measure in the Minkowski space-time, satisfying a suitable covariance condition with respect to the Poincare' group. This POV measure determines the probability that a measurement of the coordinates of the event gives results belonging to a given set in space-time. We show that this measure must vanish on the vacuum and the one-particle states, which cannot define any event. We give a general expression for the Poincare' covariant POV measures. We define the baricentric events, which lie on the world-line of the centre-of-mass, and we find a simple expression for the average values of their coordinates. Finally, we discuss the conditions which permit the determination of the coordinates with an arbitrary accuracy.Comment: 31 pages, latex, no figure

Reflexive Binding and Attitudes de se

In this paper we develop an analysis of reflexive binding involving the reflexive zibun in Japanese. We argue that the reflexive zibun is bound by a POV (point of view) holder that minimally c-commands zibun. The POV holder is defined as an argument (typically subject and Experiencer) that can be a locus of de se belief. Some predicates are incapable of hosting POV holders thus defined in combination with zibun and we call such predicates \u27anti-reflexive\u27 predicates, which are marked as such in the lexicon. De se interpretation plays a key role in both local and long distance binding of zibun

State Determination and Sufficiency of Observables

Informational completeness and the possibility of state distinction and determination are among the more important issues of quantum statistics. We use spectral and semispectral (POV) measures to analyse these questions. For a given W ∗-algebra and a family of normal states on it we investigate the relation between sufficiency in Petz’s sense of a W ∗-subalgebra generated by a spectral measure, and the possibility of determination of these states by means of an observabl