Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH223
Module Title: Mathematical Risk Theory
Module Level: Level 2
Module Credits: 5.00
Semester: SEM2
Originating Department: Mathematical Sciences
Pre-requisites: MTH113

 Aims The module provides mathematical, probabilistic and statistical techniques to construct and assess the risk models for the insurers. The students are required to be familiar with severity, frequency, aggregate and ruin models. The students are also expected to know the steps in the modeling processes, understand the assumptions in the each family of models, construct risk models given a business application, and appropriately adjust the models for insurance coverage modifications.
 Learning outcomes A Explain the concepts of decision theory and apply them.B Determine severity distributions with different insurance packageC Find frequency distributionsD Apply formulas for the aggregate models to calculate the premiums E Evaluate the impact of losses on the premiums for the different insurance policiesF Analyze the risk reassures and know how to apply them to manage riskG Formulate ruin probability and calculate it for simple cases
 Method of teaching and learning This module is delivered through formal lectures and tutorial classes
 Syllabus • Decision TheoryOptimum strategies, loss/risk functions, expected utility principle, rationality principles and the likelihood principle of optimal strategies, Minimax criterion, proper Bayes rules, model selection, the travel insurance example.• Applications of Probability Theory to actuarial risk modelsSeverity modelsMoments, percentiles, generating function, changes in parameters, classes of distributions and their relationship, creating new families of distributions by multiplication, raising to a power, exponentiation and mixing, • Frequency modelsPoisson, mixed Poisson, binomial, negative binomial, the (a,b,0) class, geometric distribution etc., truncation and modification at zero, compound frequency models and mixtures thereof.• The collective risk model (aggregate loss models)The compound risk model for aggregate claims, convolutions for the calculation of the distribution function and the probability function of the compound risk model, the moment generating function and the probability generating function of the aforementioned model, mean and variance calculation of the compound risk model, the compound Poisson risk model, the compound binomial risk model, the compound geometric risk model, sums of independent compound Poisson random variables, the compound risk model from the insurer/reinsurer point of view for simple forms of proportional and stop‐loss reinsurance (subject to a deductible), net stop‐loss premiums, the R (a, b, 0) family of distributions (satisfy Panjer's equation) for the random variable corresponding to the number of claims (frequency distribution), the probability function recursion (Panjer's recursion) of the total aggregate losses [for the class R (a, b, 0).
Delivery Hours
 Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total Hours/Semester 39 13 98 150

## Assessment

 Sequence Method % of Final Mark
 Module Catalogue generated from SITS CUT-OFF: 12/10/2019 12:21:55 AM