Program Overview

ACST3058 Survival Models

Unit Description

This unit provides sophisticated statistical and probabilistic models for survival, sickness, insurance losses, and other actuarial problems based on survival data. Techniques of survival analysis are used to estimate survival and loss distributions and evaluate risk factors in actuarial applications. Methods of both nonparametric and parametric estimation are utilized. Advanced models based on Markov chains and processes will be introduced to capture the features of stochastic transitions between different survival or loss states and to estimate the transition rates. Methods for valuing cashflows that are contingent upon multiple transition events and methods of projecting and valuing such expected cashflows will also be covered.

Unit Convenor and Teaching Staff

• Unit Convenor: Yanlin Shi
• Credit points: 10
• Prerequisites: ACST2055 and STAT2372
• Corequisites: None
• Co-badged status: None

Learning Outcomes

On successful completion of this unit, students will be able to:

• Apply and analyze different types of survival models and justify their connections with practical actuarial problems.
• Apply statistical inference techniques to estimate parameters and probability distributions of survival models.
• Demonstrate an understanding of the concepts and properties of Markov processes.
• Solve Markov transition probabilities via matrix theory and differential equations.
• Perform valuation of cashflows that are contingent upon multiple transition/decrement events.

Assessment Tasks

• Assignment (20%): A quantitative analysis task requiring detailed solutions using the statistical package R.
• Class Test (20%): A quiz/test held during class time.
• Final Exam (60%): A three-hour written paper with ten minutes reading time, to be held during the University Examination period.

Delivery and Resources

Please refer to the unit's learning management system for details on delivery and resources.

Unit Schedule

The unit schedule is as follows:

• Week 1: Probability models (revision); Survival analysis
• Week 2: Estimation of survival distributions
• Week 3: Variance estimation and confidence intervals
• Week 4: Cox proportional hazards models
• Week 5: Cox proportional hazards models; Stochastic processes
• Week 6: Markov chains
• Week 7: Markov chains; Due date for Individual Assignment
• Week 8: Markov jump processes; Class test
• Week 9: Markov jump processes
• Week 10: Applications of Markov processes
• Week 11: Applications of Markov processes
• Week 12: Competitive risks and multiple decrement tables
• Week 13: Revision

Policies and Procedures

Macquarie University policies and procedures are accessible from the university's policy central. Students should be aware of the following policies in particular with regard to Learning and Teaching:

• Academic Appeals Policy
• Academic Integrity Policy
• Academic Progression Policy
• Assessment Policy
• Fitness to Practice Procedure
• Assessment Procedure
• Complaints Resolution Procedure for Students and Members of the Public
• Special Consideration Policy

Academic Integrity

At Macquarie, academic integrity honesty, respect, trust, responsibility, fairness, and courage is at the core of learning, teaching, and research. The university recognizes that meeting the expectations required to complete assessments can be challenging and offers a range of resources and services to help students reach their potential.