Actuarial Models

MATH69511 Actuarial Models 15 Semester 1 Postgraduate Taught Level 6 Jennifer Sexton Unit coordinator Department of Mathematics 1 FHEQ level (Framework for Higher Education Qualifications) ' Masters/Integrated Masters P4 ' European Credit Transfer & Accumulation System Rating : 7.5 This course unit is primarily concerned with models for life contingent and life related contingent risks and the statistical estimation of transition rates in such models. The course starts with an introduction of Markovian models for transition between multiple states (e.g. alive, ill, dead ) and their properties. It then proceeds to develop and use such models in the context of life related insurance and other actuarial statistics, looking at the principles of valuation of benefits, policies and reserves and the calculation of premiums. The estimation of and statistical tests of mortality rates within such models are then looked at. This course unit is primarily concerned with models for life contingent and life related contingent risks and the statistical estimation of transition rates in such models. The course starts with an introduction of Markovian models for transition between multiple states (e.g. alive, ill, dead ) and their properties. It then proceeds to develop and use such models in the context of life related insurance and other actuarial statistics, looking at the principles of valuation of benefits, policies and reserves and the calculation of premiums. The estimation of and statistical tests of mortality rates within such models are then looked at. The first aim is to provide a theoretical foundation of Markov chains and their applications to various areas of actuarial science. The second aim is to introduce some classical actuarial methods of estimating mortality. Upon successful completion, the students are expected to: <ul> <li> Given a description in words of a particular application where things change randomly over time, be able to construct a Markov chain that serves as a model for this application.</li> <li> Be able to derive and/or compute probabilities, expectations and distributions associated with a Markov chain given a description of these quantities in words.</li> <li> Given some data of a time homogeneous Markov chain be able to estimate its transition intensities and probabilities via maximum likelihood.</li> <li> Be able to use the census approximation in order to estimate mortality rates given census data.</li> <li> Be able to carry out certain tests commonly used in practice in order to verify whether a given graduation of mortality rates is successful.</li> <li> Be able to compute expected present values of cash flows associated with a Markov chain or a life insurance policy given a description of such cash flows in words.</li> </ul> <ul> <li align="left"> Discrete time Markov chains: stochastic processes, transition probabilities, time homogeneity, limiting behaviour</li> <li align="left"> Markov jump processes: Kolmogorov forward equations, construction, holding times, estimation of transition rates</li> <li align="left"> Graduation: Poisson model, crude rates, exposed to risk, statistical tests</li> <li align="left"> Expected present values: state- and time-dependent premiums and benefits, reserves, discrete and continuous time Markov chain models, life insurance policies involving multiple lives</li> </ul>   0 Other 20% 1 Written exam 80% <ul> <li> Coursework 20%</li> <li> Examination 80%.</li></ul> Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework also provides an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.   N There is no reccomended reading for this module Lectures 33 Tutorials 11 0 106 This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  Please see Blackboard / course unit related emails for any further updates.