No Arbitrage and the Growth Optimal Portfolio

Abstract

Recently, several papers have expressed an interest in applying the Growth Optimal Portfolio (GOP) for pricing derivatives. We show that the existence of a GOP is equivalent to the existence of a strictly positive martingale density. Our approach circumvents two assumptions usually set forth in the literature: 1) infinite expected growth rates are permitted and 2) the market does not need to admit an equivalent martingale measure. In particular, our approach shows that models featuring credit constrained arbitrage may still allow a GOP to exist because this type of arbitrage can be removed by a change of numéraire. However, if the GOP exists the market admits an equivalent martingale measure under some numéraire and hence derivatives can be priced. The structure of martingale densities is used to provide a new characterization of the GOP which emphasizes the relation to other methods of pricing in incomplete markets. The case where GOP denominated asset prices are strict supermartingales is analyzed in the case of pure jump driven uncertainty.     

Entanglement generated by dissipation and steady state entanglement of two macroscopic objects

Entanglement is a striking feature of quantum mechanics and an essential ingredient in most applications in quantum information. Typically, coupling of a system to an environment inhibits entanglement, particularly in macroscopic systems. Here we report on an experiment where dissipation continuously generates entanglement between two macroscopic objects. This is achieved by engineering the dissipation using laser and magnetic fields, and leads to robust event-ready entanglement maintained for 0.04 s at room temperature. Our system consists of two ensembles containing about 10(12) atoms and separated by 0.5 m coupled to the environment composed of the vacuum modes of the electromagnetic field. By combining the dissipative mechanism with a continuous measurement, steady state entanglement is continuously generated and observed for up to 1 h.     

Three-Body Phase Shift in One-Dimensional 2 + 1 Scattering

For a model of three particles on a line, subject to attractive delta-function interactions, we consider the phase shift. We do this from the point of view of the calculation of the S-matrix in a hyperspherical adiabatic basis (an adiabatic S-matrix), and for energies ranging from the (negative) energy of the two-body bound state to a total energy of zero. We derive analytical expansions and present numerical work, for different approximations, and compare with the exact results that we obtain from the work of McGuire, whose model we have borrowed. We show that the simplest adiabatic approximation gives results that are qualitatively wrong, but that better approximations yield, for most of our range, excellent agreement with the exact result. Understanding the threshold behaviour, however, requires a zero-energy three-body bound state, or resonance, previously unsuspected for this model. The methods developed for the case of the simplest adiabatic approximation also yield threshold and low-energy results applicable to the two-body problem in two dimensions. Received December 23, 1996; revised May 13, 1997; accepted for publication June 19, 1997     

Projections of quantum observables onto classical degrees of freedom in mixed quantum-classical simulations: understanding linear response failure for the photoexcited hydrated electron

We present a general analytic method for understanding how specific motions of a classical bath influence the dynamics of quantum-mechanical observables in mixed quantum-classical molecular dynamics simulations. We apply our method and develop expressions for the special case of quantum solvation, allowing us to examine how specific classical solvent motions couple to the equilibrium energy fluctuations and nonequilibrium energy relaxation of a quantum-mechanical solute. As a first application of our formalism, we investigate the motions of classical water underlying the equilibrium and nonequilibrium excited-state solvent response functions of the hydrated electron; the results allow us to explain why the linear response approximation fails for this system.     

Influence of the Particle Morphology on the Activity of Nanometer Platinum Aerosol Catalysts

For nanoparticle agglomerates, the catalytic activity may depend strongly on their structure. The influence of different parameters such as agglomerate structure, primary particle temperature history and surface preconditioning on the catalytic activity of nanoparticles was investigated. The fraction of agglomerate surface contributing to the reaction depends on the agglomerate structure and on the velocity of the reaction under investigation. For extremely fast reactions such as the oxidation of hydrogen on Pt nanoparticles, only the outermost surface (exposed surface) contributes substantially to the formation of water. For the system investigated here, the inner surface not substantially contributing to the reaction accounted for at least 70% of the total particle surface as determined from oxygen presaturation experiments of the agglomerate surface. A considerable activity loss of the platinum particles was observed on preheating the nanoparticle agglomerates. The preheating leads to an increase in the nanoparticle size by an order of magnitude due to sintering. It is unclear if this activity reduction is due to changes in the particle surface state or to a real size effect of the nanoparticles.     

On The Correlation Of Binary M-sequences

We obtain the upper bound O(2^14n/15 n^−1/5) on the number of distinct values of all possible correlation functions between M-sequences of order n .     

Partially dynamic vehicle routing—models and algorithms

In this paper we propose a framework for dynamic routing systems based on their degree of dynamism. Next, we consider its impact on solution methodology and quality. Specifically, we introduce the Partially Dynamic Travelling Repairman Problem and describe several dynamic policies to minimize routing costs. The results of our computational study indicate that increasing the dynamic level results in a linear increase in route length for all policies studied. Furthermore, a Nearest Neighbour policy performed, on the average, uniformly better than the other dispatching rules studied. Among these, a Partitioning policy produced only slightly higher average route lengths.     

An improved protocol for the preparation of 3-pyridyl- and some arylboronic acids

3-Pyridylboronic acid was prepared in high yield and bulk quantity from 3-bromopyridine via a protocol of lithium-halogen exchange and "in situ quench". This technique was further studied and evaluated on other aryl halides in the preparation of arylboronic acids.     

Nowhere monotone functions and functions of nonmonotonic type

We investigate the relationships between the notions of a continuous function being monotone on no interval, monotone at no point, of monotonic type on no interval, and of monotonic type at no point. In particular, we characterize the set of all points at which a function that has one of the weaker properties fails to have one of the stronger properties. A theorem of Garg about level sets of continuous, nowhere monotone functions is strengthened by placing control on the location in the domain where the level sets are large. It is shown that every continuous function that is of monotonic type on no interval has large intersection with every function in some second category set in each of the spaces , and .