Registry
Module Specifications
Archived Version 2023 - 2024
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Description This course is designed to give students strong practical and theoretical foundations in Monte Carlo methods with an emphasis on applications relevant to insurance and finance. Each week will consist of 2 hours of lectures/tutorials and 2 hours of computer labs. The emphasis will be on using mathematical theory to justify our approaches to solving practical programming problems which have real-world relevance. The primary applications for our methods will be frequency and severity pricing in insurance, interest rate modelling, and option pricing. This module covers practical parts for the topic "Stochastic Processes" from the IFoA subject CS2. Students are expected to know the statements of important results and interpret them but lengthy and technical proofs will not be required. Programming will be done in R; this is not primarily a coding module and the only requirement is that students write clear readable code. | |||||||||||||||||||||||||||||||||||||
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Learning Outcomes 1. Apply basic results from probability theory to study the efficiency and appropriateness of Monte Carlo methods 2. Identify suitable methods for generating pseudorandom numbers 3. Use uniform random numbers to simulate random numbers of a given distribution 4. Analyse and interpret stochastic differential equations; approximate their solutions with appropriate discrete time processes for quantitative purposes 5. Write R code to simulate random variables and solutions to stochastic differential equations, empirically test pseudorandom number generators, and price options 6. Write R code to simulate Markov processes to perform applications in finance and insurance 7. Apply the theory of the Markov process to practical tasks in insurance and finance | |||||||||||||||||||||||||||||||||||||
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml |
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Indicative Content and
Learning Activities Review of Probability TheorySigma-algebras, random variables, distribution functions, limit theorems, modes of convergenceGenerating Random NumbersUniform random numbers, linear congruential generators, Chi-square and Kolmogorov-Smirnov tests, inverse transform method, acceptance rejection method, applications to Markov chains and jump processesIntroduction to the Monte Carlo MethodStrong law of large numbers, confidence intervals, error estimationIntroduction to Stochastic Differential EquationsBrownian motion – theory and simulation, motivation for SDEs, the Ito integral, Ito’s lemma, existence and uniqueness of solutionsDiscretising and Simulating Stochastic Differential EquationsEuler-Maruyama and Milstein Schemes, strong and weak orders of convergenceApplications in FinanceOption pricing, interest rate modelling, frequency and severity pricing in insurance | |||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources None | |||||||||||||||||||||||||||||||||||||
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