Jump-Diffusion Risk-Sensitive Asset Management I: Diffusion Factor Model

This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The criterion, following earlier work by Bielecki, Pliska, Nagai and others, is risk-sensitive optimization (equivalent to maximizing the expected growth rate subject to a constraint on variance.) By using a change of measure technique introduced by Kuroda and Nagai we show that the problem reduces to solving a certain stochastic control problem in the factor process, which has no jumps. The main result of the paper is to show that the risk-sensitive jump diffusion problem can be fully characterized in terms of a parabolic Hamilton-Jacobi-Bellman PDE rather than a PIDE, and that this PDE admits a classical C^{1,2} solution.Comment: 33 page

Escaping the \u3cem\u3eSporhase\u3c/em\u3e Maze: Protecting State Waters within the Commerce Clause

Eastern states, though they have enjoyed a history of relatively abundant water, increasingly face the need to conserve water, particularly to protect water-dependent ecosystems. At the same time, growing water demands, climate change, and an emerging water-oriented economy have intensified pressure for interstate water transfers. Thus, even traditionally wet states are seeking to protect or secure their water supplies. However, restrictions on water sales and exports risk running afoul of the Dormant Commerce Clause. This Article offers guidance for states, partciularly eastern states concerned with maintaining and improving water-dependent ecosystems, in seeking to restrict water exports while staying within the confines of the Dormant Commerce Clause

Nanotechnology and cancer

The biological picture of cancer is rapidly advancing from models built from phenomenological descriptions to network models derived from systems biology, which can capture the evolving pathophysiology of the disease at the molecular level. The translation of this (still academic) picture into a clinically relevant framework can be enabling for the war on cancer, but it is a scientific and technological challenge. In this review, we discuss emerging in vitro diagnostic technologies and therapeutic approaches that are being developed to handle this challenge. Our discussion of in vitro diagnostics is guided by the theme of making large numbers of measurements accurately, sensitively, and at very low cost. We discuss diagnostic approaches based on microfluidics and nanotechnology. We then review the current state of the art of nanoparticle-based therapeutics that have reached the clinic. The goal of the presentation is to identify nanotherapeutic strategies that are designed to increase efficacy while simultaneously minimizing the toxic side effects commonly associated with cancer chemotherapies

Pathwise Stochastic Calculus with Local Times

We study a notion of local time for a continuous path, defined as a limit of suitable discrete quantities along a general sequence of partitions of the time interval. Our approach subsumes other existing definitions and agrees with the usual (stochastic) local times a.s. for paths of a continuous semimartingale. We establish pathwise version of the It\^o-Tanaka, change of variables and change of time formulae. We provide equivalent conditions for existence of pathwise local time. Finally, we study in detail how the limiting objects, the quadratic variation and the local time, depend on the choice of partitions. In particular, we show that an arbitrary given non-decreasing process can be achieved a.s. by the pathwise quadratic variation of a standard Brownian motion for a suitable sequence of (random) partitions; however, such degenerate behavior is excluded when the partitions are constructed from stopping times.Comment: minor change

Conductivity of Mono- and Divalent Cations in the Microporous Zincosilicate VPI-9

Impedance spectroscopy is used to investigate the long-range ionic conductivity of the microporous, zincosilicate VPI-9 (Si/Zn = 4.0) (International Zeolite Association framework type VNI) containing the alkali cations Li^+, Na^+, K^+, Rb^+, and Cs^+, and the alkaline earth cations Mg^(2+), Ca^(2+), and Sr^(2+). Monovalent cation-exchanged samples Li- and Na-VPI-9 lose X-ray crystallinity upon vacuum dehydration at 450 °C, whereas K-, Rb-, and Cs-VPI-9 remain crystalline and exhibit conductivities of 1.7 × 10^(−4), 3.5 × 10^(−4), and 4.9 × 10^(−4) S/cm, respectively, at 450 °C and activation energies of 0.72, 0.64, and 0.69 eV, respectively, in the temperature range 150−450 °C. Divalent cation-exchanged sample Mg-VPI-9 also loses X-ray crystallinity, but Ca- and Sr-VPI-9 remain crystalline and exhibit conductivities of 2.3 × 10^(−6) S/cm and 7.7 × 10^(−7) S/cm, respectively, at 450 °C, and activation energies of 0.88 and 0.91 eV, respectively, over the temperature range 150−450 °C. When compared to aluminosilicate zeolite X (Si/Al = 1.25) exchanged with the same cations, all crystalline M-VPI-9 materials have greater conductivities than M-X, with the exception of K-X (1.6 × 10^(−3) S/cm at 450 °C), with the greatest differences arising between the divalent exchanged materials. Dense, crystalline zincosilicate samples with the compositions K_2ZnSi_xO_(2(x+1)) (x = 2−5), Rb_2ZnSi_5O_(12), and Cs_2ZnSi_5O_(12) are also prepared and characterized for comparison with the microporous materials and exhibit much lower conductivities than their microporous counterparts at the same composition