I am a mathematician working in the fields of infinite dimensional analysis, theory of point processes and random measures, and noncommutative (quantum) probability.
My most recent works have been on infinite dimensional basis-free umbral calculus and non-Abelian anyon quasiparticles.
An introduction to fundamental probabilistic concepts and methods such as probability spaces, expectation and variance of random variables, independence, law of large numbers.
This module will introduce students to sections 3, 4 and 6 of the Institute and Faculty of Actuaries CM2 syllabus. This module serves as an introduction to the Black-Scholes model for the continuous-time dynamics of a financial market containing a bank account and several kinds of stocks. This theory is based on stochastic (Itô) calculus for Brownian motion. Special attention is paid to the applications of stochastic calculus to the absence of arbitrage in a financial market and pricing and hedging of the options.
The module serves as an introduction to the main concepts, results and examples of functional analysis that are related to Banach and Hilbert spaces and bounded linear operators in them. The students will study in depth several classes of linear operators, including self-adjoint operators, unitary operators and Hilbert-Schmidt operators. The concept of the spectrum of a bounded linear operator will be introduced and studies, and the students will be taught how to practically find the spectrum.
This module will introduce students to sections 3, 4 and 6 of the Institute and Faculty of Actuaries CM2 syllabus. This module serves as an introduction to the Black-Scholes model for the continuous-time dynamics of a financial market containing a bank account and several kinds of stocks. This theory is based on stochastic (Itô) calculus for Brownian motion. Special attention is paid to the applications of stochastic calculus to the absence of arbitrage in a financial market and pricing and hedging of the options.
An introduction to Functional Analysis
A research project selected from an area of expertise of a member of staff in the Department of Mathematics. It will enable the students to develop an enquiring, analytical critical and creative approach to problem identification and solution. The project will typically focus on a subject area covered within one of the taught modules in the MRes scheme.
