The race to computing power increases every day in the simulation community. A few years ago, scientists have started to harness the computing power of Graphics Processing Units (GPUs) to parallelize their simulations. As with any parallel architecture, not only the simulation model implementation has to be ported to the new parallel platform, but all the tools must be reimplemented as well. In the particular case of stochastic simulations, one of the major element of the implementation is the pseudorandom numbers source. Employing pseudorandom numbers in parallel applications is not a straightforward task, and it has to be done with caution in order not to introduce biases in the results of the simulation. This problematic has been studied since parallel architectures are available and is called pseudorandom stream distribution. While the literature is full of solutions to handle pseudorandom stream distribution on CPU-based parallel platforms, the young GPU programming community cannot display the same experience yet. In this thesis, we study how to correctly distribute pseudorandom streams on GPU. From the existing solutions, we identified a need for good software engineering solutions, coupled to sound theoretical choices in the implementation. We propose a set of guidelines to follow when a PRNG has to be ported to GPU, and put these advice into practice in a software library called ShoveRand. This library is used in a stochastic Polymer Folding model that we have implemented in C++/CUDA. Pseudorandom streams distribution on manycore architectures is also one of our concerns. It resulted in a contribution named TaskLocalRandom, which targets parallel Java applications using pseudorandom numbers and task frameworks. Eventually, we share a reflection on the methods to choose the right parallel platform for a given application. In this way, we propose to automatically build prototypes of the parallel application running on a wide set of architectures. This approach relies on existing software engineering tools from the Java and Scala community, most of them generating OpenCL source code from a high-level abstraction layer.

Modelling and simulation are essential to modern research in cell biology. This thesis follows a journey starting from the construction of new stochastic methods for discrete biochemical systems to using them to simulate a population of interacting haematopoietic stem cell lineages. The first part of this thesis is on discrete stochastic methods. We develop two new methods, the stochastic extrapolation framework and the Stochastic Bulirsch-Stoer methods. These are based on the Richardson extrapolation technique, which is widely used in ordinary differential equation solvers. We believed that it would also be useful in the stochastic regime, and this turned out to be true. The stochastic extrapolation framework is a scheme that admits any stochastic method with a fixed stepsize and known global error expansion. It can improve the weak order of the moments of these methods by cancelling the leading terms in the global error. Using numerical simulations, we demonstrate that this is the case up to second order, and postulate that this also follows for higher order. Our simulations show that extrapolation can greatly improve the accuracy of a numerical method. The Stochastic Bulirsch-Stoer method is another highly accurate stochastic solver. Furthermore, using numerical simulations we find that it is able to better retain its high accuracy for larger timesteps than competing methods, meaning it remains accurate even when simulation time is speeded up. This is a useful property for simulating the complex systems that researchers are often interested in today. The second part of the thesis is concerned with modelling a haematopoietic stem cell system, which consists of many interacting niche lineages. We use a vectorised tau-leap method to examine the differences between a deterministic and a stochastic model of the system, and investigate how coupling niche lineages affects the dynamics of the system at the homeostatic state as well as after a perturbation. We find that larger coupling allows the system to find the optimal steady state blood cell levels. In addition, when the perturbation is applied randomly to the entire system, larger coupling also results in smaller post-perturbation cell fluctuations compared to non-coupled cells. In brief, this thesis contains four main sets of contributions: two new high-accuracy discrete stochastic methods that have been numerically tested, an improvement that can be used with any leaping method that introduces vectorisation as well as how to use a common stepsize adapting scheme, and an investigation of the effects of coupling lineages in a heterogeneous population of haematopoietic stem cell niche lineages.

É muito comum modelar problemas em finanças com processos estocásticos, dada a incerteza de suas variáveis de análise. Além disso, problemas reais nesse domínio são, em geral, de grande custo computacional, o que sugere a utilização de plataformas de alto desempenho (HPC) em sua implementação. As novas gerações de arquitetura de hardware gráfico (GPU) possibilitam a programação de propósito geral enquanto mantêm alta banda de memória e grande poder computacional. Assim, esse tipo de arquitetura vem se mostrando como uma excelente alternativa em HPC. Com isso, a proposta principal desse trabalho é estudar o ferramental matemático e computacional necessário para modelagem estocástica em finanças com a utilização de GPUs como plataforma de aceleração. Para isso, apresentamos a GPU como uma plataforma de computação de propósito geral. Em seguida, analisamos uma variedade de geradores de números aleatórios, tanto em arquitetura sequencial quanto paralela. Além disso, apresentamos os conceitos fundamentais de Cálculo Estocástico e de método de Monte Carlo para simulação estocástica em finanças. Ao final, apresentamos dois estudos de casos de problemas em finanças: \"Stops Ótimos\" e \"Cálculo de Risco de Mercado\". No primeiro caso, resolvemos o problema de otimização de obtenção do ganho ótimo em uma estratégia de negociação de ações de \"Stop Gain\". A solução proposta é escalável e de paralelização inerente em GPU. Para o segundo caso, propomos um algoritmo paralelo para cálculo de risco de mercado, bem como técnicas para melhorar a solução obtida. Nos nossos experimentos, houve uma melhora de 4 vezes na qualidade da simulação estocástica e uma aceleração de mais de 50 vezes. / Given the uncertainty of their variables, it is common to model financial problems with stochastic processes. Furthermore, real problems in this area have a high computational cost. This suggests the use of High Performance Computing (HPC) to handle them. New generations of graphics hardware (GPU) enable general purpose computing while maintaining high memory bandwidth and large computing power. Therefore, this type of architecture is an excellent alternative in HPC and comptutational finance. The main purpose of this work is to study the computational and mathematical tools needed for stochastic modeling in finance using GPUs. We present GPUs as a platform for general purpose computing. We then analyze a variety of random number generators, both in sequential and parallel architectures, and introduce the fundamental mathematical tools for Stochastic Calculus and Monte Carlo simulation. With this background, we present two case studies in finance: ``Optimal Trading Stops\'\' and ``Market Risk Management\'\'. In the first case, we solve the problem of obtaining the optimal gain on a stock trading strategy of ``Stop Gain\'\'. The proposed solution is scalable and with inherent parallelism on GPU. For the second case, we propose a parallel algorithm to compute market risk, as well as techniques for improving the quality of the solutions. In our experiments, there was a 4 times improvement in the quality of stochastic simulation and an acceleration of over 50 times.

Using a bioeconomic model and stochastic simulation to assess the economic viability of small-scale, recirculating shrimp farms in the Midwestern U.S. A series of stress tests were implemented on key input variables including survival rate, selling price, electricity usage, discount rate and the cost of added salt. The key output variable is the Net Present Value of the operation. <div><br></div><div><br></div>

Agrarmärkte sind oft durch Unsicherheit gekennzeichnet - hervorgerufen vor allem durch Zufallsschwankungen in Angebot und Nachfrage. Das Ziel der vorliegenden Studie besteht darin, die Konsequenzen solcher Unsicherheiten für die Bewertung und Gestaltung der vor einer grundlegenden Neuausrichtung stehenden EU-Milchmarktpolitik zu untersuchen. Zunächst legen empirische Betrachtungen anhand der Zeitreihen verschiedener Marktgrößen nahe, dass Unsicherheit für die Akteure auf dem EU-Milchmarkt tatsächlich ein relevantes Phänomen ist. So sind etwa Preisschwankungen trotz der auf eine Marktstabilisierung ausgerichteten staatlichen Eingriffe zu beobachten. Anhaltspunkte konnten auch zu den Ursachen der Marktunsicherheiten gewonnen werden. Während Angebot und Nachfrage in der EU eine eher stabile Entwicklung aufweisen, neigen die internationalen Milchproduktmärkte zu Fluktuationen. Zur Analyse der Auswirkungen staatlicher Eingriffe auf dem Milchmarkt bei Unsicherheit dient ein stochastisches partielles Marktgleichgewichtsmodell. Das Modell bildet die spezifischen Strukturen des Milchmarkts mit dem Rohmilchangebot, der Milchverarbeitung und der Nachfrage nach den verschiedenen Milchprodukten ab. Zur Integration von Unsicherheit wird die Modellstruktur um stochastische Variablen in den Angebots- und Nachfragefunktionen erweitert. Mit Quotenregelung, Zöllen und Exporterstattungen lassen sich wesentliche Politikinstrumente untersuchen. Gegenstand der Betrachtungen sind mögliche Auswirkungen einer neuen multilateralen Handelsvereinbarung im Rahmen der Welthandelsorganisation (WTO) sowie die Effekte dreier für den Milchmarkt formulierter Politikszenarien. Diese Politikoptionen sind die im Juni 2003 in Luxemburg beschlossene Agrarreform, eine in der Fachöffentlichkeit oft diskutierte Quotenkürzung und eine vollständige Liberalisierung des Milchmarkts samt Quotenabschaffung. Die Ergebnisse zeigen, dass veränderte Preis- und Mengeneingriffe nicht nur zu Verschiebungen im Niveau von Zielgrößen, wie beispielsweise von Erzeugerpreisen und Erlösen in der EU und auf Drittlandsmärkten führen, sondern ebenso zu veränderten Streuungen. Zusätzliche Einsichten vermitteln die Ergebnisse darüber hinaus bezüglich der Unsicherheit in der Planung der öffentlichen Ausgaben am Milchmarkt und in der Vorhersage der Wohlfahrtseffekte von Politikänderungen. Gegenüber einer deterministischen Betrachtung wird eine Politikanalyse am Milchmarkt unter expliziter Berücksichtigung von Unsicherheit damit komplexer und die Beurteilung von Politikoptionen differenzierter.