A pénzügyi eszközök árazásának alaptétele, lokálisan korlátos szemimartingál árfolyamok esetén (The fundamental theorem of asset pricing for locally bounded semimartingales)

A pénzügyi eszközök árazásának alaptétele - kissé pongyolán megfogalmazva - azt állítja, hogy egy értékpapírpiacon akkor nincs arbitrázs, ha létezik egy az eredetivel ekvivalens valószínűségi mérték, amelyre vonatkozóan az értékpapírok árait leíró folyamat egy bizonyos értelemben "martingál". Az első ilyen jellegű állítást M. Harrison és S. R. Pliska bizonyították arra esetre, amikor a valószínűségi mező végesen generált. Azóta a tételnek számos általánosítása született. Ezek közül az egyik legismertebb a Dalang{Morton{ Willinger-tétel, ami már teljesen általános valószínűségi mezőből indul ki, de felteszi, hogy az időparaméter diszkrét, és az időhorizont véges. Időközben a tételnek számos folytonos időparaméterű folyamatokra vonatkozó változata is született. Az alaptételt általános esetben, vagyis amikor valószínűségi mező teljesen általános, és az értékpapírok piaci árait leíró folyamat lokálisan korlátos szemimartingál, Delbaen és W. Schachermayer bizonyították be. A Delbaen{Schachermayer-féle alaptétel a maga nemében egy igen általános áll ítás. A tétel bizonyítása igen hosszadalmas, és a funkcionálanalízis valamint a sztochasztikus folyamatok általános elméletének mély eredményeit használja. Utóbbi tudományterület nagy részét P. A. Meyer és a francia strassbourgi iskola matematikusai dolgozták ki a 60-as évek végétől kezdve. A terület megértését tehát alaposan megnehezíti, hogy a felhasznált matematikai apparátus viszonylag friss, egy része pedig csak francia nyelven érhető el. Meggyőződésünk szerint az eredeti, 1994-es Delbaen és Schachermayer-féle bizonyítás csak kevesek által hozzáférhető. A tételnek tudomásunk szerint azóta sem született tankönyvi feldolgozása, annak ellenére, hogy maga az állítás közgazdász körökben is széles körben ismerté vált, és az eredeti cikket számos szerző idézi. Az itt bemutatott bizonyítás Delbaen és Schachermayer 1992 és 2006 közötti írásain alapul. ______ The Delbaen and Schachermayer's theorem is one of the deepest results of mathematical finance. In this article we tried to rethink and slightly simplify the original proof of the theorem to make understandable for nonspecialists who are familiar with general theory of stochastic processes. We give a detailed proof of the theorem and we give new proofs for some of the used statements.

A comparison of a distance education and locally based course in an urban university setting

The purpose of this research was to compare the academic performance and attitudes of students at the instructor-based site of a televised course and the distant site. An earlier pilot program indicated the need for certain technical and structural interventions at the distant site such as multiple "press-to-touch" microphones, a site-administrator and participative seating arrangements. At the beginning of the class, demographic data were collected from the students at both sites through a questionnaire and supplemented with information from students' records. Factors such as age, gender, ethnicity, marital status, number of children, current class status, major, work status and CLAST scores (achievement tests) were examined. There were no significant differences between the students at the sites except ethnicity and reading CLAST scores. The instructor-based site had a higher percentage of Hispanic students and the distant site had a larger percentage of Caucasian and Black Americans. The distant site scored significantly better on the reading section of the CLAST achievement test. An evaluation instrument was distributed to both sites, at the midpoint of the semester, measuring their attitude toward the organizational, technical, and pedagogical factors of the course. A second evaluation instrument, measuring similar factors, but more in-depth, was distributed to both sites near the end of the term. Nine students at the distant site were interviewed along with the site administrator to collect additional information.^ Course completion rates, dropout rates, pass rates and final grades of students at both sites were compared. There were no significant differences in academic performance between the students at both sites, however, there were significant differences in their attitudes. Those at the instructor-based site gave better ratings to most of items in the evaluation instruments. Problems at the distant site included audio and visual clarity, lack of available assistance, too much nonrelated talking, not enough opportunities to ask questions or to interact with the instructor during class. ^

Soft power as the new norm: How the Chinese-Russian strategic partnership (soft) balances American hegemony in an era of unipolarity

This study explores how great powers not allied with the United States formulate their grand strategies in a unipolar international system. Specifically, it analyzes the strategies China and Russia have developed to deal with U.S. hegemony by examining how Moscow and Beijing have responded to American intervention in Central Asia. The study argues that China and Russia have adopted a soft balancing strategy of to indirectly balance the United States at the regional level. This strategy uses normative capabilities such as soft power, alternative institutions and regionalization to offset the overwhelming material hardware of the hegemon. The theoretical and methodological approach of this dissertation is neoclassical realism. Chinese and Russian balancing efforts against the United States are based on their domestic dynamics as well as systemic constraints. Neoclassical realism provides a bridge between the internal characteristics of states and the environment which those states are situated. Because China and Russia do not have the hardware (military or economic power) to directly challenge the United States, they must resort to their software (soft power and norms) to indirectly counter American preferences and set the agenda to obtain their own interests. Neoclassical realism maintains that soft power is an extension of hard power and a reflection of the internal makeup of states. The dissertation uses the heuristic case study method to demonstrate the efficacy of soft balancing. Such case studies help to facilitate theory construction and are not necessarily the demonstrable final say on how states behave under given contexts. Nevertheless, it finds that China and Russia have increased their soft power to counterbalance the United States in certain regions of the world, Central Asia in particular. The conclusion explains how soft balancing can be integrated into the overall balance-of-power framework to explain Chinese and Russian responses to U.S. hegemony. It also suggests that an analysis of norms and soft power should be integrated into the study of grand strategy, including both foreign policy and military doctrine.

Norm-based comparison of SF -12 physical and mental health scale scores for a sample of employees of Broward County

In the new health paradigm, the connotation of health has extended beyond the measures of morbidity and mortality to include wellness and quality of life. Comprehensive assessments of health go beyond traditional biological indicators to include measures of physical and mental health status, social role-functioning, and general health perceptions. To meet these challenges, tools for assessment and outcome evaluation are being designed to collect information about functioning and well-being from the individual's point of view.^ The purpose of this study was to profile the physical and mental health status of a sample of county government employees against U.S. population norms. A second purpose of the study was to determine if significant relationships existed between respondent characteristics and personal health practices, lifestyle and other health how the tools and methods used in this investigation can be used to guide program development and facilitate monitoring of health promotion initiatives.^ The SF-12 Health Survey (Ware, Kosinski, & Keller, 1995), a validated measure of health status, was administered to a convenience sample of 450 employees attending one of nine health fairs at an urban worksite. The instrument has been utilized nationally which enabled a comparative analysis of findings of this study with national results.^ Results from this study demonstrated that several respondent characteristics and personal health practices were associated with a greater percentage of physical and/or mental scale scores that were significantly "worse" or significantly "better" than the general population. Respondent characteristics that were significantly related to the SF-12 physical and/or mental health scale scores were gender, age, education, ethnicity, and income status. Personal health practices that were significantly related to SF-12 physical and/or mental scale scores were frequency of vigorous exercise, presence of chronic illness, being at one's prescribed height and weight, eating breakfast, smoking and drinking status. This study provides an illustration of the methods used to analyze and interpret SF-12 Health Survey data, using norm-based interpretation guidelines which are useful for purposes of program development and collecting information on health at the community level. ^

Locally recurrent functions, density topologies and algebraic genericity

We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.

On the autonomous norm on the group of Hamiltonian diffeomorphisms of the torus

27 pages, 6 figures

Locally recurrent functions, density topologies and algebraic genericity

We study the algebraic and topological genericity of certain subsets of locally recurrent functions, obtaining (among other results) algebrability and spaceability within these classes.

Essays on Microeconometrics

My dissertation has three chapters which develop and apply microeconometric tech- niques to empirically relevant problems. All the chapters examines the robustness issues (e.g., measurement error and model misspecification) in the econometric anal- ysis. The first chapter studies the identifying power of an instrumental variable in the nonparametric heterogeneous treatment effect framework when a binary treat- ment variable is mismeasured and endogenous. I characterize the sharp identified set for the local average treatment effect under the following two assumptions: (1) the exclusion restriction of an instrument and (2) deterministic monotonicity of the true treatment variable in the instrument. The identification strategy allows for general measurement error. Notably, (i) the measurement error is nonclassical, (ii) it can be endogenous, and (iii) no assumptions are imposed on the marginal distribution of the measurement error, so that I do not need to assume the accuracy of the measure- ment. Based on the partial identification result, I provide a consistent confidence interval for the local average treatment effect with uniformly valid size control. I also show that the identification strategy can incorporate repeated measurements to narrow the identified set, even if the repeated measurements themselves are endoge- nous. Using the the National Longitudinal Study of the High School Class of 1972, I demonstrate that my new methodology can produce nontrivial bounds for the return to college attendance when attendance is mismeasured and endogenous.

The second chapter, which is a part of a coauthored project with Federico Bugni, considers the problem of inference in dynamic discrete choice problems when the structural model is locally misspecified. We consider two popular classes of estimators for dynamic discrete choice models: K-step maximum likelihood estimators (K-ML) and K-step minimum distance estimators (K-MD), where K denotes the number of policy iterations employed in the estimation problem. These estimator classes include popular estimators such as Rust (1987)’s nested fixed point estimator, Hotz and Miller (1993)’s conditional choice probability estimator, Aguirregabiria and Mira (2002)’s nested algorithm estimator, and Pesendorfer and Schmidt-Dengler (2008)’s least squares estimator. We derive and compare the asymptotic distributions of K- ML and K-MD estimators when the model is arbitrarily locally misspecified and we obtain three main results. In the absence of misspecification, Aguirregabiria and Mira (2002) show that all K-ML estimators are asymptotically equivalent regardless of the choice of K. Our first result shows that this finding extends to a locally misspecified model, regardless of the degree of local misspecification. As a second result, we show that an analogous result holds for all K-MD estimators, i.e., all K- MD estimator are asymptotically equivalent regardless of the choice of K. Our third and final result is to compare K-MD and K-ML estimators in terms of asymptotic mean squared error. Under local misspecification, the optimally weighted K-MD estimator depends on the unknown asymptotic bias and is no longer feasible. In turn, feasible K-MD estimators could have an asymptotic mean squared error that is higher or lower than that of the K-ML estimators. To demonstrate the relevance of our asymptotic analysis, we illustrate our findings using in a simulation exercise based on a misspecified version of Rust (1987) bus engine problem.

The last chapter investigates the causal effect of the Omnibus Budget Reconcil- iation Act of 1993, which caused the biggest change to the EITC in its history, on unemployment and labor force participation among single mothers. Unemployment and labor force participation are difficult to define for a few reasons, for example, be- cause of marginally attached workers. Instead of searching for the unique definition for each of these two concepts, this chapter bounds unemployment and labor force participation by observable variables and, as a result, considers various competing definitions of these two concepts simultaneously. This bounding strategy leads to partial identification of the treatment effect. The inference results depend on the construction of the bounds, but they imply positive effect on labor force participa- tion and negligible effect on unemployment. The results imply that the difference- in-difference result based on the BLS definition of unemployment can be misleading

due to misclassification of unemployment.

Linear Hyperspectral Unmixing Using L0-norm Approximations and Nonnegative Matrix Factorization

Spectral unmixing (SU) is a technique to characterize mixed pixels of the hyperspectral images measured by remote sensors. Most of the existing spectral unmixing algorithms are developed using the linear mixing models. Since the number of endmembers/materials present at each mixed pixel is normally scanty compared with the number of total endmembers (the dimension of spectral library), the problem becomes sparse. This thesis introduces sparse hyperspectral unmixing methods for the linear mixing model through two different scenarios. In the first scenario, the library of spectral signatures is assumed to be known and the main problem is to find the minimum number of endmembers under a reasonable small approximation error. Mathematically, the corresponding problem is called the $\ell_0$-norm problem which is NP-hard problem. Our main study for the first part of thesis is to find more accurate and reliable approximations of $\ell_0$-norm term and propose sparse unmixing methods via such approximations. The resulting methods are shown considerable improvements to reconstruct the fractional abundances of endmembers in comparison with state-of-the-art methods such as having lower reconstruction errors. In the second part of the thesis, the first scenario (i.e., dictionary-aided semiblind unmixing scheme) will be generalized as the blind unmixing scenario that the library of spectral signatures is also estimated. We apply the nonnegative matrix factorization (NMF) method for proposing new unmixing methods due to its noticeable supports such as considering the nonnegativity constraints of two decomposed matrices. Furthermore, we introduce new cost functions through some statistical and physical features of spectral signatures of materials (SSoM) and hyperspectral pixels such as the collaborative property of hyperspectral pixels and the mathematical representation of the concentrated energy of SSoM for the first few subbands. Finally, we introduce sparse unmixing methods for the blind scenario and evaluate the efficiency of the proposed methods via simulations over synthetic and real hyperspectral data sets. The results illustrate considerable enhancements to estimate the spectral library of materials and their fractional abundances such as smaller values of spectral angle distance (SAD) and abundance angle distance (AAD) as well.

Locally quasi-nilpotent elementary operators

Let A be a unital dense algebra of linear mappings on a complex vector space X. Let φ = Σⁿ _i=1 M_ai,_bi be a locally quasi-nilpotent elementary operator of length n on A. We show that, if {a1, . . . , an} is locally linearly independent, then the local dimension of V (φ) = span{b_ia_j : 1 ≤ i, j ≤ n} is at most n(n−1) 2 . If ldim V (φ) = n(n−1) 2 , then there exists a representation of φ as φ = Σⁿ _i=1 M_ui,_vi with v_iu_j = 0 for i ≥ j. Moreover, we give a complete characterization of locally quasinilpotent elementary operators of length 3.

Prognostic role of the LCS6 KRAS variant in locally advanced rectal cancer: results of the EXPERT-C trial.

Background: Lethal-7 (let-7) is a tumour suppressor miRNA which acts by down-regulating several oncogenes including KRAS. A single-nucleotide polymorphism (rs61764370, T > G base substitution) in the let-7 complementary site 6 (LCS-6) of KRAS mRNA has been shown to predict prognosis in early-stage colorectal cancer (CRC) and benefit from anti-epidermal growth factor receptor monoclonal antibodies in metastatic CRC. Patients and methods: We analysed rs61764370 in EXPERT-C, a randomised phase II trial of neoadjuvant CAPOX followed by chemoradiotherapy, surgery and adjuvant CAPOX plus or minus cetuximab in locally advanced rectal cancer. DNA was isolated from formalin-fixed paraffin-embedded tumour tissue and genotyped using a PCR-based commercially available assay. Kaplan–Meier method and Cox regression analysis were used to calculate survival estimates and compare treatment arms. Results: A total of 155/164 (94.5%) patients were successfully analysed, of whom 123 (79.4%) and 32 (20.6%) had the LCS-6 TT and LCS-6 TG genotype, respectively. Carriers of the G allele were found to have a statistically significantly higher rate of complete response (CR) after neoadjuvant therapy (28.1% versus 10.6%; P = 0.020) and a trend for better 5-year progression-free survival (PFS) [77.4% versus 64.5%: hazard ratio (HR) 0.56; P = 0.152] and overall survival (OS) rates (80.3% versus 71.9%: HR 0.59; P = 0.234). Both CR and survival outcomes were independent of the use of cetuximab. The negative prognostic effect associated with KRAS mutation appeared to be stronger in patients with the LCS-6 TT genotype (HR PFS 1.70, P = 0.078; HR OS 1.79, P = 0.082) compared with those with the LCS-6 TG genotype (HR PFS 1.33, P = 0.713; HR OS 1.01, P = 0.995). Conclusion: This analysis suggests that rs61764370 may be a biomarker of response to neoadjuvant treatment and an indicator of favourable outcome in locally advanced rectal cancer possibly by mitigating the poor prognosis of KRAS mutation. In this setting, however, this polymorphism does not appear to predict cetuximab benefit.

RAS mutations and cetuximab in locally advanced rectal cancer: results of the EXPERT-C trial.

Background: RAS mutations predict resistance to anti-epidermal growthfactor receptor (EGFR) monoclonal antibodies in metastatic colorectal cancer. We analysed RAS mutations in 30 non-metastatic rectal cancer patients treated with or without cetuximab within the 31 EXPERT-C trial.

Methods: Ninety of 149 patients with tumours available for analysis were KRAS/BRAF wild-type, and randomly assigned to capecitabine plus oxaliplatin (CAPOX) followed by chemoradiotherapy, surgery and adjuvant CAPOX or the same regimen plus cetuximab (CAPOX-C). Of these, four had a mutation of NRAS exon 3, and 84 were retrospectively analysed for additional KRAS (exon 4) and NRAS (exons 2/4) mutations by using bi-directional Sanger sequencing. The effect of cetuximab on study end-points in the RAS wild-type population was analysed.

Results: Eleven (13%) of 84 patients initially classified as KRAS/BRAF wild-type were found to have a mutation in KRAS exon 4 (11%) or NRAS exons 2/4 (2%). Overall, 78/149 (52%) assessable patients were RAS wild-type (CAPOX, n = 40; CAPOX-C, n = 38). In this population, after a median follow-up of 63.8 months, in line with the initial analysis, the addition of cetuximab was associated with numerically higher, but not statistically significant, rates of complete response (15.8% versus 7.5%, p = 0.31), 5-year progression-free survival (75.5% versus 67.5%, hazard ratio (HR) 0.61, p = 0.25) and 5-year overall survival (83.8% versus 70%, HR 0.54, p = 0.20).

Conclusions: RAS mutations beyond KRAS exon 2 and 3 were identified in 17% of locally advanced rectal cancer patients. Given the small sample size, no definitive conclusions on the effect of additional RAS mutations on cetuximab treatment in this setting can be drawn and further investigation of RAS in larger studies is warranted.