Market models with optimal arbitrage

We construct and study market models admitting optimal arbitrage. We say that a model admits optimal arbitrage if it is possible, in a zero-interest rate setting, starting with an initial wealth of 1 and using only positive portfolios, to superreplicate a constant c>1. The optimal arbitrage strategy is the strategy for which this constant has the highest possible value. Our definition of optimal arbitrage is similar to the one in Fernholz and Karatzas (2010), where optimal relative arbitrage with respect to the market portfolio is studied. In this work we present a systematic method to construct market models where the optimal arbitrage strategy exists and is known explicitly. We then develop several new examples of market models with arbitrage, which are based on economic agents' views concerning the impossibility of certain events rather than ad hoc constructions. We also explore the concept of fragility of arbitrage introduced in Guasoni and Rasonyi (2012), and provide new examples of arbitrage models which are not fragile in this sense

Tight Upper Bound Of The Maximum Speed Of Evolution Of A Quantum State

I report a tight upper bound of the maximum speed of evolution from one quantum state $\rho$ to another $\rho'$ with fidelity $F(\rho,\rho')$ less than or equal to an arbitrary but fixed value under the action of a time-independent Hamiltonian. Since the bound is directly proportional to the average absolute deviation from the median of the energy of the state ${\mathscr D}E$, one may interpret ${\mathscr D}E$ as a meaningful measure of the maximum information processing capability of a system.Comment: 4 pages, 1 figure, minor changes with an additional reference added, to appear in PR

Robust utility maximization in markets with transaction costs

We consider a continuous-time market with proportional transaction costs. Under appropriate assumptions we prove the existence of optimal strategies for investors who maximize their worst-case utility over a class of possible models. We consider utility functions defined either on the positive axis or on the whole real line

Self-checking on-line testable static RAM

This is a fault-tolerant random access memory for use in fault-tolerant computers. It comprises a plurality of memory chips each comprising a plurality of on-line testable and correctable memory cells disposed in rows and columns for holding individually addressable binary bits and provision for error detection incorporated into each memory cell for outputting an error signal whenever a transient error occurs therein. In one embodiment, each of the memory cells comprises a pair of static memory sub-cells for simultaneously receiving and holding a common binary data bit written to the memory cell and the error detection provision comprises comparator logic for continuously sensing and comparing the contents of the memory sub-cells to one another and for outputting the error signal whenever the contents do not match. In another embodiment, each of the memory cells comprises a static memory sub-cell and a dynamic memory sub-cell for simultaneously receiving and holding a common binary data bit written to the memory cell and the error detection provision comprises comparator logic for continuously sensing and comparing the contents of the static memory sub-cell to the dynamic memory sub-cell and for outputting the error signal whenever the contents do not match. Capability for correction of errors is also included

Optimal investment with intermediate consumption under no unbounded profit with bounded risk

We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. We show that the key conclusions of the utility maximization theory hold under the assumptions of no unbounded profit with bounded risk (NUPBR) and of the finiteness of both primal and dual value functions.Comment: 10 pages, revised version, to appear in the Applied Probability Journal

Relation Between Quantum Speed Limits And Metrics On U(n)

Recently, Chau [Quant. Inform. & Comp. 11, 721 (2011)] found a family of metrics and pseudo-metrics on $n$-dimensional unitary operators that can be interpreted as the minimum resources (given by certain tight quantum speed limit bounds) needed to transform one unitary operator to another. This result is closely related to the weighted $\ell^1$-norm on ${\mathbb R}^n$. Here we generalize this finding by showing that every weighted $\ell^p$-norm on ${\mathbb R}^n$ with 1\le p \le \limitingp induces a metric and a pseudo-metric on $n$-dimensional unitary operators with quantum information-theoretic meanings related to certain tight quantum speed limit bounds. Besides, we investigate how far the correspondence between the existence of metrics and pseudo-metrics of this type and the quantum speed limits can go.Comment: minor amendments, 6 pages, to appear in J.Phys.

The Influence of 3D Porous Chitosan-Alginate Biomaterial Scaffold Properties on the Behavior of Breast Cancer Cells

The tumor microenvironment plays an important role in regulating cancer cell behavior. The tumor microenvironment describes the cancer cells, and the surrounding endothelial cells, fibroblasts, and mesenchymal stem cells, along with the extracellular matrix (ECM). The tumor microenvironment stiffens as cancer undergoes malignant progression, providing biophysical cues that promote invasive, metastatic cellular behaviors. This project investigated the influence of three dimensional (3D) chitosan-alginate (CA) scaffold stiffness on the morphology, growth, and migration of green fluorescent protein (GFP) – transfected MDA-MB-231 (231-GFP) breast cancer (BCa) cells. The CA scaffolds were produced by the freeze casting method at three concentrations, 2 wt%, 4 wt%, and 6 wt% to provide different stiffness culture substrates. The CA scaffold material properties were characterized using scanning electron microscopy imaging for pore structure and compression testing for Young\u27s Modulus. The BCa cell cultures were characterized at day 1, 3, and 7 timepoints using Alamar Blue assay for cell number, fluorescence imaging for cell morphology, and single-cell tracking for cell migration. Pore size calculations using SEM imaging yielded pore sizes of 253.29 ± 52.45 µm, 209.55 ± 21.46 µm, and 216.83 ± 32.63 µm for 2 wt%, 4 wt%, and 6 wt%, respectively. Compression testing of the CA scaffolds yielded Young\u27s Modulus values of 0.064 ± 0.008 kPa, 2.365 ± 0.32 kPa and 3.30 ± 0.415 kPa for 2 wt%, 4 wt%, and 6 wt% CA scaffolds, respectively. The results showed no significant difference in cell number among the 3D CA scaffold groups. However, the 231-GFP cells cultured in 2 wt% CA scaffolds possessed greater cellular size, area, perimeter, and lower cellular circularity compared to those in 4 wt% and 6 wt% CA scaffolds, suggesting a more prominent presence of cell clusters in softer substrates compared to stiffer substrates. The results also showed cells in 6 wt% CA having a higher average cell migration speed compared to those in 2 wt% and 4 wt% CA scaffolds, indicating a positive relationship between substrate stiffness and cell migration velocity. Findings from this experiment may contribute to the development of enhanced in vitro 3D breast tumor models for basic cancer research using 3D porous biomaterial scaffolds