Study of the risk-adjusted pricing methodology model with methods of Geometrical Analysis

Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie group analysis we obtain the Lie algebra admitted by the RAPM equation. It gives us the possibility to describe an optimal system of subalgebras and correspondingly the set of invariant solutions to the model. In this way we can describe the complete set of possible reductions of the nonlinear RAPM model. Reductions are given in the form of different second order ordinary differential equations. In all cases we provide solutions to these equations in an exact or parametric form. We discuss the properties of these reductions and the corresponding invariant solutions.Comment: larger version with exact solutions, corrected typos, 13 pages, Symposium on Optimal Stopping in Abo/Turku 200

Nonlinear Parabolic Equations arising in Mathematical Finance

This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existence and uniqueness of solutions. In the numerical part we discuss a stable finite-volume and finite difference schemes for solving fully nonlinear parabolic equations.Comment: arXiv admin note: substantial text overlap with arXiv:1603.0387

Common variable immunodeficiency syndrome with right aortic arch: a case report

BACKGROUND: Common variable immunodificiency syndrome predominantly affects adults. It is characterized by low production of all the major classes of immunoglobulins. We report a case of common variable immunodeficiency syndrome with right aortic arch. An association of right-sided arch and common variable immunodificiency syndrome has not been previously reported. CASE PRESENTATION: A 41-year-old female patient presented with a history of recurrent pneumonia, sinusitis, otitis media, diarrhoea, cystitis since childhood. Biochemical and immunocytochemical analysis revealed common variable immunodeficiency syndrome and radiological evaluation confirmed right aortic arch and aberrant left subclavian artery. CONCLUSION: Common variable immunodeficiency syndrome syndrome is a clinical entity that should be kept in mind in patients with recurrent infections of different sites

Moving boundary transformation for American call options with transaction cost: Finite difference methods and computing

The pricing of American call option with transaction cost is a free boundary problem. Using a new transformation method the boundary is made to follow a certain known trajectory in time. The new transformed problem is solved by various finite difference methods, such as explicit and implicit schemes. Broyden’s and Schubert’s methods are applied as a modification to Newton’s method in the case of nonlinearity in the equation. An alternating direction explicit method with second-order accuracy in time is used as an example in this paper to demonstrate the technique. Numerical results demonstrate the efficiency and the rate of convergence of the methods

Educational Design Research in Mozambique: Starting Mathematics from Authentic Resources

This article describes a research on learner-centred instruction in Mozambique, Africa. A starting point was the use of real-life resources, such as traditional art craft objects and authentic newspaper clippings. The study used a method which is termed 'design research'. This method aligns theory with practice and is geared towards improving educational practice. In two sub-studies, On geometry and on statistics, learner-centred instruction was facilitated through the use of worksheets with open-ended questions tailored for group work. The designs were tested in cyclic interventions and formatively evaluated through observation reports, interviews and assessment of learners' work. A decentralised, student-centred learning ecology proved to be feasible in overcrowded classrooms, typical in African education

DIFFERENT MEDIA, DIFFERENT TYPES OF COLLECTIVE WORK IN ONLINE CONTINUING TEACHER EDUCATION: WOULD YOU PASS THE PEN, PLEASE?

This paper presents some findings regarding the interaction between different computer interfaces and different types of collective work. We want to claim that design in online learning environments has a paramount role in the type of collaboration that happens among participants. In this paper, we report on data that illustrate how teachers can collaborate online in order to learn how to use geometry software in teaching activities. A virtual environment which allows that construction to be carried out collectively, even if the participants are not sharing a classroom, is the setting for the research presented in this paper