Pricing of Warrants with Stock Price Dependent Threshold Conditions

Warrants with stock price dependent threshold conditions give the right to buy specially issued stocks, if the performance of the stock price satisfies some requirements. Existence of these derivatives changes the price process of the underlying. We show that in the presence of such warrants one cannot assume that the stock market is arbitrage free and that the stock is tradeable at every time moment with the same price for buying and selling. This means that the usual methods for deriving fair prices for such warrants cannot be used. We start from a simple model for the firm's value process and discuss some ways to specify a related model for the stock price process in the presence of warrants with threshold conditions. We also discuss how indifference pricing approach can be used for pricing such warrants

READING COMPETENCE AND ENGAGEMENT OF LATVIAN STUDENTS IN THE VIEW OF OECD PISA 2018 RESULTS

Students' reading competence determines the achievements of learners in all areas of school education as well as in their further education, professional activity and life. The results of the OECD Program for International Student Assessment - OECD PISA 2018 confirm the need to improve reading competence in Latvia (OECD, 2019).The aim of the study is to analyze the achievement of Latvia's fifteen-year-old students in OECD PISA 2018 and the previous international program cycles in relation to students' reading engagement and its changes. Reading engagement significantly influences not only students' reading competence but are in themselves one of the goals of modern education (Guthrie Wigfield, 2000; Guthrie, Klauda Ho, 2013). The study will use the OECD PISA international databases for statistical analysis the data of Latvia and other countries for comparisons with OECD averages, and especially with the attitudes and achievements of Estonian and Finnish students. The analysis of the first results shows that the promotion of reading engagement among Latvian students, especially boys, is one of the factors for increasing reading competence.

Promocijas darbs

Elektroniskā versija nesatur pielikumusAtslēgas vārdi: domāšana, matemātiskā domāšana, kognitīvā darbība, intelekts Promocijas darba ‘’Matemātiskās domāšanas iespējas augstākā izglītībā profesionālās kompetences veidošanā” pirmajā nodaļā sniegts domāšanas teorijas skaidrojums pamatojoties uz aksioloģisko teoriju ar akcentuāciju uz matemātisko domāšanu. Darba otrajā nodaļā pamatojoties uz inovatīvām pārmaiņām izglītībā, domāšana aplūkota kā izziņas darbības līdzeklis un tās izpausmes matemātiskā domāšanā kognitīvā, afektīvā un sociālā aspektā. Darba trešajā nodaļā veikta teorētisko atziņu eksperimentālā pārbaude studentu intelekta spēju kontekstā: H. Gārdnera tests, Dž. Rāvena progresīvo matricu tests, profesionālās darbības motivācijas tests, mācīšanās stilu apzināšanas tests. Sniegts autora rezumējums par testu pielietošanas mērķtiecību.Key words: thinking, mathematical thinking, cognitive action, intellect Chapter 1 of the doctoral thesis „ Possibilities of mathematical thinking in higher education in formation of the professional competence” offers the explanation of the thinking theory on the basis of the axiological theory with the emphasis on the mathematical thinking. Chapter 2 of the thesis is based on the innovative changes in education and thinking is treated as a means of cognitive action and its expressions in mathematical thinking in cognitive, affective and social aspect are described. Chapter 3 of the thesis represents the experimental test of the theoretical ideas in the context of students’ intelectual abilities: H. Gardner’s test, J.Raven’s test of progressive matrixes, the motivation test of professional activity, test for identifying the learning styles. The thesis also presents the author’s summary on the purposefulness of applying the tests

On Attribute-Based Encryption for Circuits from Multilinear Maps

Töös antakse ülevaade atribuudipõhisest krüpteerimisest. Tutvustatakse Garg et al artiklis "Attribute-Based Encryption for Circuits from Multilinear Maps" esitatud konstruktsiooni. Tehakse ka mõned ettepanekud antud konstruktsiooni parandamiseks, ja tõestatakse saadud konstruktsiooni turvalisus.In this work, an overview of Attribute-Based Encryption is given. A recent construction given by Garg et al in the paper "Attribute-Based Encryption for Circuits from Multilinear Maps" is introduced. Some improvements are suggested for that construction, and the security of the resulting scheme is proved

Computational Finance

Course "Computational Finance" gives an overview different partial differential equations arising in mathematical finance, their derivation procedures and numerical solution methods. In the computer labs students acquire practical skills for computing the prices of various financial options.BeSt programmi toetusel loodud e-kursuse "Computational Finance" õppematerjalid. Kursuse sisuks on finantsoptsioonide hindu kirjeldavate võrrandite tuletamine, nende lahendamiseks erinevate numbriliste meetodite konstrueerimine ning arvutiprogrammina realiseerimine. Materjalid sisaldavad loengukonspekti, praktikumide juhendeid ning näitelahendusi programmeerimiskeeles Python

Promotion of Reading Interests in the Study Process at the University and Lessons in School

The necessity of promoting reading interests in connection with the problems that have to be solved today and in near future in school, university and the society on the whole puts forward the task for the prospective teachers of literature to master not only theoretical knowledge in their study process but also to acquire skills necessary for their future pedagogical work so that they are able to choose the most suitable methodological approach for the interpretation of a literary work in each teaching/learning situation

MATHEMATICAL MODELING OF DIFFUSION BOUNDARY PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS USING MATLAB AND C++ FOR NUMERICAL AND ANALYTICAL SOLUTIONS

The article examines a second-order parabolic partial differential equation of a three-dimensional (3D) non-stationary boundary problem with constant diffusion coefficients and periodic boundary conditions in the x and y directions. The method for reducing the (3D) non-stationary boundary problem to the corresponding one-dimensional (1D) non-stationary boundary problem using periodic boundary conditions in the x and y directions is discussed. The stationary (analytical) solution of the obtained (1D) stationary boundary problem is also obtained. The numerical solutions of the 1D boundary problem are obtained using the Matlab package "pdepe" and the C++ programming language. As a practical application of the developed mathematical model, the article discusses calculating the concentration of heavy metal Ca in a peat layer based on the obtained experimental data (measurements)