ETC5343 · Financial mathematics under uncertainty

Overview

Financial Mathematics under uncertainty will cover the topics of Markov chain, Markov process, survival models, mortality estimation, graduation, censoring, mortality projection, and machine learning applications.

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

Learning outcomes

1. describe and classify stochastic processes including counting processes and understand state and time spaces and mixed processes
2. define and apply the Markov Chain and Chapman-Kolmogorov equation; understand the stationary distribution, experience rating systems, time homo and inhomo-geneous Markov Chains and application of such as modelling tools
3. define and apply a Markov process. Understand the poisson process as a counting process derive and solve Kolmogorov equations, understand and solve multiple state models including the HSD model, generalise to models where transition also depends on duration of stay in a state and describe how to model using such models
4. explain concept of survival models, lifetime models, distribution and density functions for future lifetime, force of mortality, actuarial notation, life expectancy (complete and curtate) and the two-state model
5. describe estimation procedures for lifetime distributions. Identify censoring by types and problems caused by censoring; understand and apply the Nelson-Aalen and Kaplan-Meier estimation procedures and the Cox proportional hazards model
6. derive maximum likelihood estimators for transition intensities and functions for constant transition models
7. estimate transition intensities dependent on age (exact or census); understand the principle of correspondence, calculate central and initial exposures, explain the concept of rate intervals, estimate initial and central mortality rates from census data and death data
8. describe and carry out graduation of mortality data and understand and apply graduation tests
9. describe approaches to forecasting mortality rates; discuss some of the more commonly used forecasting approaches including p-splines, time series modelling and APC models.

Workload

Minimum total expected workload to achieve the learning outcomes for this unit is 144 hours per semester typically comprising a mixture of scheduled learning activities and independent study. Independent study may include associated readings, assessment and preparation for scheduled activities. You are expected to complete all pre-class activities prior to your scheduled class, and post-class activities should be completed after your scheduled class. Learning activities may include a combination of teacher directed, peer directed and online engagement activities.

Student experience, not official rules. Nothing here changes what the Handbook says.