Exam 1986 pdf

Exam and solutions in PDF

Exam 1985 pdf

Exam and solutions in PDF

Exercise sheet 2

Exercises and solutions in LaTex

Exam 1984 pdf

Exam and solutions in PDF

Exam 1983 pdf

Exam and solutions in PDF

MA348exam 1998

Exam questions and solutions in LaTex

MA348exam 1998 pdf

Exam questions and solutions in PDF

Exam 1987

Exam and solutions in LaTex

Exam 1986

Exam and solutions in LaTex

Exam 1988

Exam and solutions in LaTex

Ecuaciones diferenciales estocásticas con condición final y soluciones de viscosidad de EDPS semilineales de segundo orden

El objetivo de este documento es recopilar algunos resultados clasicos sobre existencia y unicidad ´ de soluciones de ecuaciones diferenciales estocasticas (EDEs) con condici ´ on final (en ingl ´ es´ Backward stochastic differential equations) con particular enfasis en el caso de coeficientes mon ´ otonos, y su cone- ´ xion con soluciones de viscosidad de sistemas de ecuaciones diferenciales parciales (EDPs) parab ´ olicas ´ y el´ıpticas semilineales de segundo orden.

Medical image registration based on random line sampling

One of the key aspects in 3D-image registration is the computation of the joint intensity histogram. We propose a new approach to compute this histogram using uniformly distributed random lines to sample stochastically the overlapping volume between two 3D-images. The intensity values are captured from the lines at evenly spaced positions, taking an initial random offset different for each line. This method provides us with an accurate, robust and fast mutual information-based registration. The interpolation effects are drastically reduced, due to the stochastic nature of the line generation, and the alignment process is also accelerated. The results obtained show a better performance of the introduced method than the classic computation of the joint histogram

Hedging effectiveness of total returns swaps: application to the Japanese market

The development of the real estate swap market offers many opportunities for investors to adjust the exposure of their portfolios to real estate. A number of OTC transactions have been observed in markets around the world. In this paper we examine the Japanese commercial real estate market from the point of view of an investor holding a portfolio of properties seeking to reduce the portfolio exposure to the real estate market by swapping an index of real estate for LIBOR. This paper explores the practicalities of hedging portfolios comprising small numbers of individual properties against an appropriate index. We use the returns from 74 properties owned by Japanese Real Estate Investment Trusts over the period up to September 2007. The paper also discusses and applies the appropriate stochastic processes required to model real estate returns in this application and presents alternative ways of reporting hedging effectiveness. We find that the development of the derivative does provide the capacity for hedging market risk but that the effectiveness of the hedge varies considerably over time. We explore the factors that cause this variability.

Law of large numbers for super-brownian motions with a single point source

We investigate the super-Brownian motion with a single point source in dimensions 2 and 3 as constructed by Fleischmann and Mueller in 2004. Using analytic facts we derive the long time behavior of the mean in dimension 2 and 3 thereby complementing previous work of Fleischmann, Mueller and Vogt. Using spectral theory and martingale arguments we prove a version of the strong law of large numbers for the two dimensional superprocess with a single point source and finite variance.