### 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 Year CATS Level Semester CATS Value Session 2021-22 Level 6 FHEQ Second Semester 15

### Aims

Provide a solid grounding in GLM and Bayesian credibility theory.
Provide good knowledge in time series including applications.
Provide an introduction to machine learning techniques.
Demonstrate how to apply software R to solve questions
Prepare students adequately to sit for the exams in CS1 and CS2 of the Institute and Faculty of Actuaries.

### Learning Outcomes

(LO1) Be able to explain concepts of Bayesian statistics and calculate Bayesian estimators.

(LO2) Be able to state the assumptions of the GLM models - normal linear model, understand the properties of the exponential family.

(LO3) Be able to apply time series to various problems.

(LO4) Understand some machine learning techniques.

(LO5) Be confident in solving problems in R.

(S1) Problem solving skills

(S2) Numeracy

### Syllabus

(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.

### 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

### Assessment

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    50