Stochastic Processes

Exercises, exams and solutions for a second year maths course.

Java computer modelling of the Earth System

The JModel suite consists of a number of models of aspects of the Earth System. The Java programmes model in detail aspects of the cycles of some major biogeochemical elements that exemplify the range of geochemical processes in marine environments.

The Modelling Journey

These were slides developed as part of our work with the JISC Community Engagement Team and CETIS to introduce people to different forms of system modelling, including scenarios and personas, soft systems methods, UML (Use cases, activity diagrams and sequence diagrams), BMPN and EA modelling with Archimate.

Modelling for Problem Solving in the Large

This a short presentation which introduces how models and modelling help us to solve large scale problems in the real world. It introduces the idea that dynamic behaviour is caused by interacting components in the system. Feedback in the system makes behaviour prediction difficult unless we use modelling to support understanding

Soft Sytems Modelling

This presentation introduces Soft Systems Modelling as a technique to support investigating the behaviour of dynamic systems in the real world. It combines techniques from General Systems Theory, Soft Systems Methodolgy and Critical Systems Heuristics. Personas and Scenarios are used as a technique for exploring the motivations of stakeholders in the systems.

Systems Design: Use Case Modelling Lab using Visual Paradigm

This lab follows the lecture 'System Design: Using UML Use Cases'http://www.edshare.soton.ac.uk/9619/ It introduces Visual Paradigm as a UML modelling tool. Students work through Visual Paradigm online Tutorials and then create two projects.

Systems Design: Activity and Sequence modelling using Visual Paradigm

This lab follows the lectures 'System Design: http://www.edshare.soton.ac.uk/9653/ and http://www.edshare.soton.ac.uk/6280/ . Students use Visual Paradigm for UML to build Activity and Sequence models through project examples: Library, Plant Nursery and a Health Spa

Alps Workshop 1 p10 Role modelling pie chart

Pie chart animation

Systems Design: Class modelling using Visual Paradigm

This lab follows the lectures 'System Design: http://www.edshare.soton.ac.uk/6280/ http://www.edshare.soton.ac.uk/9653/ and http://www.edshare.soton.ac.uk/9713/ Students use Visual Paradigm for UML to build Class models through project examples: Aircraft Manufacturing Company, Library, Plant Nursery.

WAIS Seminar:Modelling the Web: Examples of modelling language, network evolution and physical-social systems

Speaker(s): Prof. Steffen Staab Organiser: Dr Tim Chown Time: 23/05/2014 10:30-11:30 Location: B53/4025 Abstract The Web is constructed based on our experiences in a multitude of modalities: text, networks, images, physical locations are some examples. Understanding the Web requires from us that we can model these modalities as they appear on the Web. In this talk I will show some examples of how we model text, hyperlink networks and physical-social systems in order to improve our understanding and our use of the Web.

On lions, impala, and bigraphs: modelling interactions in Ubiquitous Computing

As ubiquitous systems have moved out of the lab and into the world the need to think more systematically about how there are realised has grown. This talk will present intradisciplinary work I have been engaged in with other computing colleagues on how we might develop more formal models and understanding of ubiquitous computing systems. The formal modelling of computing systems has proved valuable in areas as diverse as reliability, security and robustness. However, the emergence of ubiquitous computing raises new challenges for formal modelling due to their contextual nature and dependence on unreliable sensing systems. In this work we undertook an exploration of modelling an example ubiquitous system called the Savannah game using the approach of bigraphical rewriting systems. This required an unusual intra-disciplinary dialogue between formal computing and human- computer interaction researchers to model systematically four perspectives on Savannah: computational, physical, human and technical. Each perspective in turn drew upon a range of different modelling traditions. For example, the human perspective built upon previous work on proxemics, which uses physical distance as a means to understand interaction. In this talk I hope to show how our model explains observed inconsistencies in Savannah and ex- tend it to resolve these. I will then reflect on the need for intradisciplinary work of this form and the importance of the bigraph diagrammatic form to support this form of engagement. Speaker Biography Tom Rodden Tom Rodden (rodden.info) is a Professor of Interactive Computing at the University of Nottingham. His research brings together a range of human and technical disciplines, technologies and techniques to tackle the human, social, ethical and technical challenges involved in ubiquitous computing and the increasing used of personal data. He leads the Mixed Reality Laboratory (www.mrl.nott.ac.uk) an interdisciplinary research facility that is home of a team of over 40 researchers. He founded and currently co-directs the Horizon Digital Economy Research Institute (www.horizon.ac.uk), a university wide interdisciplinary research centre focusing on ethical use of our growing digital footprint. He has previously directed the EPSRC Equator IRC (www.equator.ac.uk) a national interdisciplinary research collaboration exploring the place of digital interaction in our everyday world. He is a fellow of the British Computer Society and the ACM and was elected to the ACM SIGCHI Academy in 2009 (http://www.sigchi.org/about/awards/).

Introduction to Soft Systems Modelling

Two lectures that introduce the idea of modelling in the large, and contrasts hard system and soft system modelling. The second lecture goes into detail on a number of specific methods for analysing a system (CATWOE and CSH) and on modelling a system (Systems Diagrams and Personas).

Valor en riesgo del portafolio de TES de los bancos colombianos

En este trabajo se realiza la medición del riesgo de mercado para el portafolio de TES de un banco colombiano determinado, abordando el pronóstico de valor en riesgo (VaR) mediante diferentes modelos multivariados de volatilidad: EWMA, GARCH ortogonal, GARCH robusto, así como distintos modelos de VaR con distribución normal y distribución t-student, evaluando su eficiencia con las metodologías de backtesting propuestas por Candelon et al. (2011) con base en el método generalizado de momentos, junto con los test de independencia y de cobertura condicional planteados por Christoffersen y Pelletier (2004) y por Berkowitz, Christoffersen y Pelletier (2010). Los resultados obtenidos demuestran que la mejor especificación del VaR para la medición del riesgo de mercado del portafolio de TES de los bancos colombianos, es el construido a partir de volatilidades EWMA y basado en la distribución normal, ya que satisface las hipótesis de cobertura no condicional, independencia y cobertura condicional, al igual que los requerimientos estipulados en Basilea II y en la normativa vigente en Colombia.

Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.