This paper familiarizes the reader with contingent convertibles and their role in the current financial landscape. A contingent convertible is a security behaving like a bond in normal times, but that converts into equity or is written down in times of turbulence. The paper presents a few existing pricing approaches and introduces an extension to one of these, the equity derivatives approach, by letting the underlying asset follow a jump-diffusion process instead of a standard Geometrical Brownian Motion. The extension requires sophisticated computational techniques in order for the pricing to stay within reasonable time frames. Since market data is sparse and incomplete in this area, the validation of the model is not performed quantitatively, but instead supported by qualitative arguments.

Este trabalho apresenta um estudo sobre a solução numérica da equação geral de advecção-difusão usando uma metodologia numérica conservativa. Para a discretização espacial, é usado o Método de Volumes Finitos devido à natureza conservativa da equação em questão. O método é configurado de modo a ter suas variáveis centradas em centro de célula e, para as variáveis, como a velocidade, centradas nas faces um método de interpolação de segunda ordem é utilizado para um ajuste numérico ao centro. Embora a implementação computacional tenha sido feita de forma paramétrica de maneira a acomodar outros esquemas numéricos, a discretização temporal dá ênfase ao Método de Crank-Nicolson. Tal método numérico, sendo ele implícito, dá origem a um sistema linear de equações que, aqui, é resolvido empregando-se o Método Multigrid-Multinível. A corretude do código implementado é verificada a partir de testes por soluções manufaturadas, de modo a checar se a ordem de convergência prevista em teoria é alcançada pelos métodos numéricos. Um jato laminar é simulado, com o acoplamento entre a equação de Navier-Stokes e a equação geral de advecção-difusão, em um domínio computacional tridimensional. O jato é uma forma de vericar se o algoritmo de geração de malhas adaptativas funciona corretamente. O módulo produzido neste trabalho é baseado no código computacional AMR3D-P desenvolvido pelos grupos de pesquisa do IME-USP e o MFLab/FEMEC-UFU (Laboratório de Dinâmica de Fluidos da Universidade Federal de Uberlândia). A linguagem FORTRAN é utilizada para o desenvolvimento da metodologia numérica e as simulações foram executadas nos computadores do LabMAP(Laboratório da Matemática Aplicada do IME-USP) e do MFLab/FEMEC-UFU. / This work presents a study about the numerical solution of variable coecients advectiondi usion equation, or simply, general advection-diusion equation using a conservative numerical methodology. The Finite Volume Method is choosen as discretisation of the spatial domain because the conservative nature of the focused equation. This method is set up to have the scalar variable in a cell centered scheme and the vector quantities, such velocity, are face centered and they need a second order interpolation to get adjusted to the cell center. The computational code is parametric, in which, any implicit temporal discretisation can be choosen, but the emphasis relies on Crank-Nicolson method, a well-known second order method. The implicit nature of aforementioned method gives a linear system of equations which is solved here by the Multilevel-Multigrid method. The correctness of the computational code is checked by manufactured solution method used to inspect if the theoretical order of convergence is attained by the numerical methods. A laminar jet is simulated, coupling the Navier-Stokes equation and the general advection-diusion equation in a 3D computational domain. The jet is a good way to check the corectness of adaptative mesh renement algorithm. The module designed here is based in a previous implemented code AMR3D-P designed by IME-USP and MFLab/FEMEC-UFU (Fluid Dynamics Laboratory, Federal University of Uberlândia). The programming language used is FORTRAN and the simulations were run in LabMAP(Applied Mathematics Laboratoy at IME-USP) and MFLab/FEMEC-UFU computers.

Este trabalho apresenta um estudo sobre a solução numérica da equação geral de advecção-difusão usando uma metodologia numérica conservativa. Para a discretização espacial, é usado o Método de Volumes Finitos devido à natureza conservativa da equação em questão. O método é configurado de modo a ter suas variáveis centradas em centro de célula e, para as variáveis, como a velocidade, centradas nas faces um método de interpolação de segunda ordem é utilizado para um ajuste numérico ao centro. Embora a implementação computacional tenha sido feita de forma paramétrica de maneira a acomodar outros esquemas numéricos, a discretização temporal dá ênfase ao Método de Crank-Nicolson. Tal método numérico, sendo ele implícito, dá origem a um sistema linear de equações que, aqui, é resolvido empregando-se o Método Multigrid-Multinível. A corretude do código implementado é verificada a partir de testes por soluções manufaturadas, de modo a checar se a ordem de convergência prevista em teoria é alcançada pelos métodos numéricos. Um jato laminar é simulado, com o acoplamento entre a equação de Navier-Stokes e a equação geral de advecção-difusão, em um domínio computacional tridimensional. O jato é uma forma de vericar se o algoritmo de geração de malhas adaptativas funciona corretamente. O módulo produzido neste trabalho é baseado no código computacional AMR3D-P desenvolvido pelos grupos de pesquisa do IME-USP e o MFLab/FEMEC-UFU (Laboratório de Dinâmica de Fluidos da Universidade Federal de Uberlândia). A linguagem FORTRAN é utilizada para o desenvolvimento da metodologia numérica e as simulações foram executadas nos computadores do LabMAP(Laboratório da Matemática Aplicada do IME-USP) e do MFLab/FEMEC-UFU. / This work presents a study about the numerical solution of variable coecients advectiondi usion equation, or simply, general advection-diusion equation using a conservative numerical methodology. The Finite Volume Method is choosen as discretisation of the spatial domain because the conservative nature of the focused equation. This method is set up to have the scalar variable in a cell centered scheme and the vector quantities, such velocity, are face centered and they need a second order interpolation to get adjusted to the cell center. The computational code is parametric, in which, any implicit temporal discretisation can be choosen, but the emphasis relies on Crank-Nicolson method, a well-known second order method. The implicit nature of aforementioned method gives a linear system of equations which is solved here by the Multilevel-Multigrid method. The correctness of the computational code is checked by manufactured solution method used to inspect if the theoretical order of convergence is attained by the numerical methods. A laminar jet is simulated, coupling the Navier-Stokes equation and the general advection-diusion equation in a 3D computational domain. The jet is a good way to check the corectness of adaptative mesh renement algorithm. The module designed here is based in a previous implemented code AMR3D-P designed by IME-USP and MFLab/FEMEC-UFU (Fluid Dynamics Laboratory, Federal University of Uberlândia). The programming language used is FORTRAN and the simulations were run in LabMAP(Applied Mathematics Laboratoy at IME-USP) and MFLab/FEMEC-UFU computers.

Red River Delta (RRD) ist einer von zwei gröÿten Flussmündungen in Vietnam. Das Gebiet ist der Ursprung des Reises in diesem Land. Die Landwirtschaft spielt eine entscheidende Rolle für die Wirtschaft Vietnams besonders im Red River Delta. In den vergangenen Jahren hat die Adoption von Neuerungen in der Landwirtschaft die Qualität und Menge der Produktion deutlich erhöht. Neue Getreidesorten wurden entwickelt, Management-, sowie Produktionsmethoden wie Integriertes Pest-Management (IPM) wurden verbessert, und Standards wie z. B. VIETGAP eingeführt. Das Forschungsprojekt konzentriert sich auf die Frage, welche Möglichkeiten bestehen, den Prozess der Übernahme von Neuerungen durch Landwirte zu verbessern. Dabei sind die sozioökonomischen Bedingungen des Gebiets zu berücksichtigen. In dem Projekt wird das vorhandene Innovationssystem bewertet um daraus die Empfehlungen für Verbesserungen abzuleiten. Das interdisziplinäre Forschungsprojekt verwendet An sätze der Diusionstheorie, des kollektiven Handelns, und einzelne Erklärungsfaktoren (z. B. kulturelle Bedingungen) um das individuelle Übernahmeverhalten erklären zu können. Die empirischen Ergebnisse der Arbeit beruhen auf 15 Experteninterviewsund 85 ausführlichen Befragungen von Kleinbauern. Die Zusammenarbeit zwischen Bauern, Beratern, Servicedienstleistern, S&T Organisationen, landwirtschaftlichen Unternehmen und NGOs wird beschrieben. In vielen Fällen geschieht der Transfer an die Bauern, durch (1) von vertraglichen Vereinbarungen zwischen den Partnern, (2) durch Anreize, oder (3) durch Lernprozesss im Anschluss an die Verbreitung der Information durch Informationsnetze. Die Rolle von Bauern in diesen Prozessen ist sowohl durch eine aktive oder passive Teilnahme gekennzeichnet. Die Landwirte werden in Gruppen eingeteilt: frühe Adopter, Imitatoren (späte Adopter) und Nichtadopter, um das Adoptionsverhalten besser erklären zu können. / The Red River Delta (RRD) is one of two biggest deltas in Vietnam. The region is the origin of paddy rice in the country. Agriculture plays a crucial role for Vietnam''s economy, especially in the RRD. Recently, adoption of innovations in agriculture has enhanced the quality and quantity of production. Old varieties of crops have been replaced, and improved management practices as well as production methods such as Integrated Pest Management (IPM), VIETGAP have been implemented. This research project focuses on the question, whether there is a need to enhance the process of innovation transfer to farmers. Socioeconomic conditions of the region have to be taken into account. The project will evaluate the existing transfer system and tries to nd out if it is possible to improve the innovation transfer by interfering into the process. The interdisciplinary research project uses the theory of diffusion of innovation, theory of collective action, and other explanations such as the cultural inuence and individual behavior. The results of this report are based on 15 expert interviews and 85 detailed questionnaires of smallholder farmers. The cooperation between farmers and agents of extension services, S&T organizations, agricultural enterprises, NGOs will be described. In some cases, the process of innovation transfer to farmers happens directly because of agreements in a contract between partners, or motivated by incentives, or simply pursuant to a learning process following diffusion of information through networks. The role of farmers in these processes is also directly observed as an active or passive participation. Farmers are classifed in groups of adopters (potential adopters, early adopters), imitators (later adopters) and non-adopters and factors to explain the adoption behavior are discussed.

In this thesis we present the Laplace transform method of option pricing and it's realization, also compare it with another methods. We consider vanilla and exotic options, but more attention we pay to the two-asset correlation options. We chose the one of the modifications of Black-Scholes model, the Kou double exponential jump-diffusion model with the double exponential distribution of jumps, as model of the underlying stock prices development. The computations was done by the Laplace transform and it's inversion by the Euler method. We will present in details proof of finding Laplace transforms of put and call two-asset correlation options, the calculations of the moment generation function of the jump-diffusion by Levy-Khintchine formulae in cases without jumps and with independent jumps, and direct calculation of the risk-neutral expectation by solving double integral. Our work also contains the programme code for two-asset correlation call and put options. We will show the realization of our programme in the real data. As a result we see how our model complies on the NASDAQ OMX Stock-holm Market, considering the two-asset correlation options on three cases by stock prices of Handelsbanken, Ericsson and index OMXS30.