# ETC5343 - Financial mathematics under uncertainty - 2019

## Postgraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Business and Economics

Organisational Unit

Department of Econometrics and Business Statistics

Chief examiner(s)

Dr Yi He (First semester)
Associate Professor Athanasios Pantelous (Second semester)

Unit guides

Offered

Clayton

• First semester 2019 (On-campus)
• Second semester 2019 (On-campus)

Prerequisites

ETC2430 or equivalent.

Prohibitions

ETC3430

## Synopsis

Financial mathematics under uncertainty will apply the ideas of interest rates, present values, cash flow modelling and profit testing in the context of certain payments and payments dependent on individual deaths or other uncertain risk. We will also introduce stochastic modelling techniques applied to actuarial and financial contexts.

Students will cover the topics of present values and accumulated values, equations of value, Markov modelling, survival models, life tables and contingent products.

## Outcomes

The learning goals associated with this unit are to:

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.

## Assessment

Within semester assessment: 40% + Examination: 60%

## Workload requirements

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. The unit requires on average three/four hours of scheduled activities per week. Scheduled activities may include a combination of teacher directed learning, peer directed learning and online engagement.

See also Unit timetable information