Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing

2000 Mathematics Subject Classification: 65M06, 65M12.

Low Volatility Options and Numerical Diffusion of Finite Difference Schemes

2000 Mathematics Subject Classification: 65M06, 65M12.

Interaction of Kelvin waves and nonlocality of energy transfer in superfluids

We argue that the physics of interacting Kelvin Waves (KWs) is highly nontrivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbuelence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a local nonlinear (partial differential) equation. This equation is much simpler for analysis and numerical simulations of KWs than the Biot-Savart equation, and in contrast to the completely integrable local induction approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Second, we show that the previously suggested Kozik-Svistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak nonlocality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.

Dinamikus optimalizálás és a Leontief-modell (Dynamic optimization and the Leontief model)

A tanulmány a variációszámítás gazdasági alkalmazásaiból ismertet hármat. Mindhárom alkalmazás a Leontief-modellen alapszik. Az optimális pályák vizsgálata után arra keressük a választ, hogy az Euler–Lagrange-differenciálegyenlet rendszerrel kapott megoldások valóban optimális megoldásai-e a modelleknek. Arra a következtetésre jut a tanulmány, hogy csak pótlólagos közgazdasági feltételek bevezetésével határozhatók meg az optimális megoldások. Ugyanakkor a megfogalmazott feltételek segítségével az ismertetett modellek egy általánosabb keretbe illeszthetők. A tanulmány végső eredménye az, hogy mind a három modell optimális megoldása a Neumann-sugárnak felel meg. /===/ The study presents three economic applications of variation calculations. All three rely on the Leontief model. After examination of the optimal courses, an answer is sought to whether the solutions to the Euler–Lagrange differential equation system are really opti-mal solutions to the models. The study concludes that the optimal solutions can only be determined by introducing additional economic conditions. At the same time, the models presented can be fitted into a general framework with the help of the conditions outlined. The final conclusion of the study is that the optimal solution of all three models fits into the Neumann band.

Derivatív pénzügyi termékek árdinamikája és az új típusú kamatlábmodellek (Interest rate models and the price processes of financial derivatives)

Ennek a cikknek az a célja, hogy áttekintést adjon annak a folyamatnak néhány főbb állomásáról, amit Black, Scholes és Merton opcióárazásról írt cikkei indítottak el a 70-es évek elején, és ami egyszerre forradalmasította a fejlett nyugati pénzügyi piacokat és a pénzügyi elméletet. / === / This review article compares the development of financial theory within and outside Hungary in the last three decades starting with the Black-Scholes revolution. Problems like the term structure of interest rate volatilities which is in the focus of many research internationally has not received the proper attention among the Hungarian economists. The article gives an overview of no-arbitrage pricing, the partial differential equation approach and the related numerical techniques, like the lattice methods in pricing financial derivatives. The relevant concepts of the martingal approach are overviewed. There is a special focus on the HJM framework of the interest rate development. The idea that the volatility and the correlation can be traded is a new horizon to the Hungarian capital market.

Lokális energiamódszer kicsi rendben gerjesztett Liénard-egyenletekre (Local energy method for little order forced equations)

Az x''+f(x) x'+g(x) = 0 alakú Liénard-típusú differenciálegyenlet központi szerepet játszik az üzleti ciklusok Káldor-Kalecki-féle [3,4] és Goodwin-féle [2] modelljeiben, sőt egy a munkanélküliség és vállalkozás-ösztönzések ciklikus változásait leíró újabb modellben [1] is. De ugyanez a nemlineáris egyenlettípus a gerjesztett ingák és elektromos rezgőkörök elméletét is felöleli [5]. Az ezzel kapcsolatos irodalom nagyrészt a határciklusok létezését vizsgálja (pl. [5]), pedig az alapvető stabilitási kérdések jóval áttekinthetőbb módon kezelhetők, s a kapott eredmények közvetve a határciklusok létezésének feltételeit is sokkal jobban be tudják határolni. Jelen dolgozatban az egyváltozós analízis hatékony nyelvezetével olyan egyszerűen megfogalmazható eredményekhez jutunk, amelyek képesek kitágítani az üzleti és más közgazdasági ciklusok modelljeinek kereteit, illetve pl. az [1]-beli modellhez újabb szemléltető speciális eseteket is nyerünk. ____ The Liénard type differential equation of the form x00 + f(x) ¢ x0 + g(x) = 0 has a central role in business cycle models by Káldor [3], Kalecki [4] and Goodwin [2], moreover in a new model describing the cyclical behavior of unemployment and entrepreneurship [1]. The same type of nonlinear equation explains the features of forced pendulums and electric circuits [5]. The related literature discusses mainly the existence of limit cycles, although the fundamental stability questions of this topic can be managed much more easily. The achieved results also outline the conditions for the existence of limit cycles. In this work, by the effective language of real valued analysis, we obtain easy-formulated results which may broaden the frames of economic and business cycle models, moreover we may gain new illustrative particular cases for e.g., [1].

Three essays on hospital efficiency

This dissertation analyzes hospital efficiency using various econometric techniques. The first essay provides additional and recent evidence to the presence of contract management behavior in the U.S. hospital industry. Unlike previous studies, which focus on either an input-demand equation or the cost function of the firm, this paper estimates the two jointly using a system of nonlinear equations. Moreover, it addresses the longitudinal problem of institutions adopting contract management in different years, by creating a matched control group of non-adopters with the same longitudinal distribution as the group under study. The estimation procedure then finds that labor, and not capital, is the preferred input in U.S. hospitals regardless of managerial contract status. With institutions that adopt contract management benefiting from lower labor inefficiencies than the simulated non-contract adopters. These results suggest that while there is a propensity for expense preference behavior towards the labor input, contract managed firms are able to introduce efficiencies over conventional, owner controlled, firms. Using data for the years 1998 through 2007, the second essay investigates the production technology and cost efficiency faced by Florida hospitals. A stochastic frontier multiproduct cost function is estimated in order to test for economies of scale, economies of scope, and relative cost efficiencies. The results suggest that small-sized hospitals experience economies of scale, while large and medium sized institutions do not. The empirical findings show that Florida hospitals enjoy significant scope economies, regardless of size. Lastly, the evidence suggests that there is a link between hospital size and relative cost efficiency. The results of the study imply that state policy makers should be focused on increasing hospital scale for smaller institutions while facilitating the expansion of multiproduct production for larger hospitals. The third and final essay employs a two staged approach in analyzing the efficiency of hospitals in the state of Florida. In the first stage, the Banker, Charnes, and Cooper model of Data Envelopment Analysis is employed in order to derive overall technical efficiency scores for each non-specialty hospital in the state. Additionally, input slacks are calculated and reported in order to identify the factors of production that each hospital may be over utilizing. In the second stage, we employ a Tobit regression model in order to analyze the effects a number of structural, managerial, and environmental factors may have on a hospital’s efficiency. The results indicated that most non-specialty hospitals in the state are operating away from the efficient production frontier. The results also indicate that the structural make up, managerial choices, and level of competition Florida hospitals face have an impact on their overall technical efficiency.

Análise do fluxo d’água na barragem Engenheiro Armando Ribeiro Gonçalves - Açu/RN

The solution of partial differential equation of seepage problems is difficult to find analytically, especially for situations that involve great complexity. To overcome this problem, software based on finite differences and finite elements are usually used. This work presents the use of a finite element software, the GEO5, to solve the seepage problem at a dam of very complex section, the dam Eng. Armando Ribeiro Gonçalves, which at the end of its construction suffered rupture of the upstream slope at the central dam and then went through a process of reconstruction and auscultation. The analyses were performed for the operating condition of the reservoir, with an established flow. A numerical model was developed based on the level readings of the reservoir water and their piezometric readings as a proposal for the evaluation and future behavior prediction of the dam on established flow conditions. The use of constitutive models with the aid of computer systems is reflected in a way to predict future risk situations so they can be prevented

Effects of seasonally varying temperature and salinity on the dynamics of sea lice (Lepeophtheirus salmonis)

Sea lice (Lepeophtheirus salmonis) are an economically significant parasite in salmonid aquaculture. They exhibit temperature-dependent development rates and salinity-dependent mortality, which can greatly impact sea lice population dynamics, but no deterministic models have incorporated these seasonal variables. To understand how seasonality affects sea lice population dynamics, I derive a delay differential equation model with temperature and salinity dependence. I find that peak reproductive output in Newfoundland and British Columbia differs by four months. A sensitivity analysis shows sea lice abundance is most sensitive to variation in mean annual water temperature and salinity, whereas it is lease sensitive to infection rate. Additionally, I investigate the effects of production cycle timing on sea lice management and find that optimal production cycle start times are between the 281st and 337th days of the year in Newfoundland. I also demonstrate that adjusting follow-up treatment timing in response to temperature can improve treatment regimes. My results suggest that effective sea lice management requires consideration of local temperature and salinity patterns.

A long non-coding RNA targets microRNA miR-34a to regulate colon cancer stem cell asymmetric division.

The roles of long non-coding RNAs (lncRNAs) in regulating cancer and stem cells are being increasingly appreciated. Its diverse mechanisms provide the regulatory network with a bigger repertoire to increase complexity. Here we report a novel LncRNA, Lnc34a, that is enriched in colon cancer stem cells (CCSCs) and initiates asymmetric division by directly targeting the microRNA miR-34a to cause its spatial imbalance. Lnc34a recruits Dnmt3a via PHB2 and HDAC1 to methylate and deacetylate the miR-34a promoter simultaneously, hence epigenetically silencing miR-34a expression independent of its upstream regulator, p53. Lnc34a levels affect CCSC self-renewal and colorectal cancer (CRC) growth in xenograft models. Lnc34a is upregulated in late-stage CRCs, contributing to epigenetic miR-34a silencing and CRC proliferation. The fact that lncRNA targets microRNA highlights the regulatory complexity of non-coding RNAs (ncRNAs), which occupy the bulk of the genome.

Essays on Job Search and Labor Market Dynamics

This dissertation consists of three separate essays on job search and labor market dynamics. In the first essay, “The Impact of Labor Market Conditions on Job Creation: Evidence from Firm Level Data”, I study how much changes in labor market conditions reduce employment fluctuations over the business cycle. Changes in labor market conditions make hiring more expensive during expansions and cheaper during recessions, creating counter-cyclical incentives for job creation. I estimate firm level elasticities of labor demand with respect to changes in labor market conditions, considering two margins: changes in labor market tightness and changes in wages. Using employer-employee matched data from Brazil, I find that all firms are more sensitive to changes in wages rather than labor market tightness, and there is substantial heterogeneity in labor demand elasticity across regions. Based on these results, I demonstrate that changes in labor market conditions reduce the variance of employment growth over the business cycle by 20% in a median region, and this effect is equally driven by changes along each margin. Moreover, I show that the magnitude of the effect of labor market conditions on employment growth can be significantly affected by economic policy. In particular, I document that the rapid growth of the national minimum wages in Brazil in 1997-2010 amplified the impact of the change in labor market conditions during local expansions and diminished this impact during local recessions.

In the second essay, “A Framework for Estimating Persistence of Local Labor

Demand Shocks”, I propose a decomposition which allows me to study the persistence of local labor demand shocks. Persistence of labor demand shocks varies across industries, and the incidence of shocks in a region depends on the regional industrial composition. As a result, less diverse regions are more likely to experience deeper shocks, but not necessarily more long lasting shocks. Building on this idea, I propose a decomposition of local labor demand shocks into idiosyncratic location shocks and nationwide industry shocks and estimate the variance and the persistence of these shocks using the Quarterly Census of Employment and Wages (QCEW) in 1990-2013.

In the third essay, “Conditional Choice Probability Estimation of Continuous- Time Job Search Models”, co-authored with Peter Arcidiacono and Arnaud Maurel, we propose a novel, computationally feasible method of estimating non-stationary job search models. Non-stationary job search models arise in many applications, where policy change can be anticipated by the workers. The most prominent example of such policy is the expiration of unemployment benefits. However, estimating these models still poses a considerable computational challenge, because of the need to solve a differential equation numerically at each step of the optimization routine. We overcome this challenge by adopting conditional choice probability methods, widely used in dynamic discrete choice literature, to job search models and show how the hazard rate out of unemployment and the distribution of the accepted wages, which can be estimated in many datasets, can be used to infer the value of unemployment. We demonstrate how to apply our method by analyzing the effect of the unemployment benefit expiration on duration of unemployment using the data from the Survey of Income and Program Participation (SIPP) in 1996-2007.

On thermodynamics in the primary power conversion of oscillating water column wave energy converters

The paper presents an investigation to the thermodynamics of the air flow in the air chamber for the oscillating water column wave energy converters, in which the oscillating water surface in the water column pressurizes or de-pressurises the air in the chamber. To study the thermodynamics and the compressibility of the air in the chamber, a method is developed in this research: the power take-off is replaced with an accepted semi-empirical relationship between the air flow rate and the oscillating water column chamber pressure, and the thermodynamic process is simplified as an isentropic process. This facilitates the use of a direct expression for the work done on the power take-off by the flowing air and the generation of a single differential equation that defines the thermodynamic process occurring inside the air chamber. Solving the differential equation, the chamber pressure can be obtained if the interior water surface motion is known or the chamber volume (thus the interior water surface motion) if the chamber pressure is known. As a result, the effects of the air compressibility can be studied. Examples given in the paper have shown the compressibility, and its effects on the power losses for large oscillating water column devices.

Epigenetic Therapy for the Treatment of Hypertension-Induced Cardiac Hypertrophy and Fibrosis

BACKGROUND: The development of heart failure is associated with changes in the size, shape, and structure of the heart that has a negative impact on cardiac function. These pathological changes involve excessive extracellular matrix deposition within the myocardial interstitium and myocyte hypertrophy. Alterations in fibroblast phenotype and myocyte activity are associated with reprogramming of gene transcriptional profiles that likely requires epigenetic alterations in chromatin structure. The aim of our work was to investigate the potential of a currently licensed anticancer epigenetic modifier as a treatment option for cardiac diseases associated with hypertension-induced cardiac hypertrophy and fibrosis.

METHODS AND RESULTS: The effects of DNA methylation inhibition with 5-azacytidine (5-aza) were examined in a human primary fibroblast cell line and in a spontaneously hypertensive rat (SHR) model. The results from this work allude to novel in vivo antifibrotic and antihypertrophic actions of 5-aza. Administration of the DNA methylation inhibitor significantly improved several echocardiographic parameters associated with hypertrophy and diastolic dysfunction. Myocardial collagen levels and myocyte size were reduced in 5-aza-treated SHRs. These findings are supported by beneficial in vitro effects in cardiac fibroblasts. Collagen I, collagen III, and α-smooth muscle actin were reduced in a human ventricular cardiac fibroblast cell line treated with 5-aza.

CONCLUSION: These findings suggest a role for epigenetic modifications in contributing to the profibrotic and hypertrophic changes evident during disease progression. Therapeutic intervention with 5-aza demonstrated favorable effects highlighting the potential use of this epigenetic modifier as a treatment option for cardiac pathologies associated with hypertrophy and fibrosis.

Characterisation of a secretory serine protease inhibitor (SjB6) from Schistosoma japonicum

BACKGROUND: Proteins belonging to the serine protease inhibitor (serpin) superfamily play essential physiological roles in many organisms. In pathogens, serpins are thought to have evolved specifically to limit host immune responses by interfering with the host immune-stimulatory signals. Serpins are less well characterised in parasitic helminths, although some are thought to be involved in mechanisms associated with host immune modulation. In this study, we cloned and partially characterised a secretory serpin from Schistosoma japonicum termed SjB6, these findings provide the basis for possible functional roles.

METHODS: SjB6 gene was identified through database mining of our previously published microarray data, cloned and detailed sequence and structural analysis and comparative modelling carried out using various bioinformatics and proteomics tools. Gene transcriptional profiling was determined by real-time PCR and the expression of native protein determined by immunoblotting. An immunological profile of the recombinant protein produced in insect cells was determined by ELISA.

RESULTS: SjB6 contains an open reading frame of 1160 base pairs that encodes a protein of 387 amino acid residues. Detailed sequence analysis, comparative modelling and structural-based alignment revealed that SjB6 contains the essential structural motifs and consensus secondary structures typical of inhibitory serpins. The presence of an N-terminal signal sequence indicated that SjB6 is a secretory protein. Real-time data indicated that SjB6 is expressed exclusively in the intra-mammalian stage of the parasite life cycle with its highest expression levels in the egg stage (p < 0.0001). The native protein is approximately 60 kDa in size and recombinant SjB6 (rSjB6) was recognised strongly by sera from rats experimentally infected with S. japonicum.

CONCLUSIONS: The significantly high expression of SjB6 in schistosome eggs, when compared to other life cycle stages, suggests a possible association with disease pathology, while the strong reactivity of sera from experimentally infected rats against rSjB6 suggests that native SjB6 is released into host tissue and induces an immune response. This study presents a comprehensive demonstration of sequence and structural-based analysis of a secretory serpin from a trematode and suggests SjB6 may be associated with important functional roles in S. japonicum, particularly in parasite modulation of the host microenvironment.

Geometric properties of 2-dimensional minimal surfaces in a sub-Riemannian manifold which models the Visual Cortex

In this paper we study the notion of degree forsubmanifolds embedded in an equiregular sub-Riemannian manifold and we provide the definition of their associated area functional. In this setting we prove that the Hausdorff dimension of a submanifold coincides with its degree, as stated by Gromov. Using these general definitions we compute the first variation for surfaces embedded in low dimensional manifolds and we obtain the partial differential equation associated to minimal surfaces. These minimal surfaces have several applications in the neurogeometry of the visual cortex.