Module Details |
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module. |
Title | Statistical Methods in Insurance and Finance | ||
Code | MATH374 | ||
Coordinator |
Dr S Sahin Mathematical Sciences Sule.Sahin@liverpool.ac.uk |
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Year | CATS Level | Semester | CATS Value |
Session 2021-22 | Level 6 FHEQ | Second Semester | 15 |
Aims |
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Provide a solid grounding in GLM and Bayesian credibility theory. |
Learning Outcomes |
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(LO1) Be able to explain concepts of Bayesian statistics and calculate Bayesian estimators. |
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(LO2) Be able to state the assumptions of the GLM models - normal linear model, understand the properties of the exponential family. |
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(LO3) Be able to apply time series to various problems. |
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(LO4) Understand some machine learning techniques. |
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(LO5) Be confident in solving problems in R. |
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(S1) Problem solving skills |
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(S2) Numeracy |
Syllabus |
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(a) GLM: Linear regression, multiple linear regression, normal linear model, GLM: the exponential family of distributions for the binomial, Poisson, exponential, Gamma, normal distribution, the Pearson and deviance residuals, application of tests in model fitting. (b) Bayesian statistics: Bayes' Theorem, prior and a posteriori distribution. Loss function, credibility premium formula, role of credibility factor, Bayesian approach to credibility theory, empirical Bayes approach to credibility theory and its use to derive credibility premiums in simple cases. (c) Time series: Serial dependence (autocorrelation, correlograms), stationary and non-stationary processes. Moving Average (MA) processes, Autoregressive (AR) processes, Autoregressive moving average processes (ARMA), extension to integrated processes (ARIMA) and non-linear processes, such as ARCH and GARCH, the multivariate autoregressive model. Concept of co-integration in time series and appl ications of time series models. (d) Machine learning: Principles of machine learning, key supervised and unsupervised machine learning techniques, explaining the difference between regression and classification and between generative and discriminative models. Applications of machine learning techniques to simple problems. |
Recommended Texts |
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Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module. |
Pre-requisites before taking this module (other modules and/or general educational/academic requirements): |
MATH101 CALCULUS I; MATH102 CALCULUS II; MATH162 INTRODUCTION TO STATISTICS; MATH263 STATISTICAL THEORY AND METHODS I; MATH264 STATISTICAL THEORY AND METHODS II; MATH103 INTRODUCTION TO LINEAR ALGEBRA |
Co-requisite modules: |
Modules for which this module is a pre-requisite: |
Programme(s) (including Year of Study) to which this module is available on a required basis: |
Programme(s) (including Year of Study) to which this module is available on an optional basis: |
Assessment |
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EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Written Exam on campus | 60 | 50 | ||||
CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
class test includes an R language component | 0 | 50 |