Stochastic Techniques in Insurance (ACTL20003)

Undergraduate level 2Points: 12.5On Campus (Parkville)

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Overview

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Semester 2
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This subject aims to provide a thorough grounding in stochastic techniques for actuarial studies. It covers some probability concepts including expectations, conditional expectations, joint and marginal distributions, moment generating function and probability generating function;  some commonly used probability distributions in insurance and finance; mixed distributions and actuarial applications; ordinary differential equations and actuarial applications; recursive techniques and actuarial applications; actuarial applications of Laws of Large Numbers and Central Limit Theorem; generating and Laplace transforms; actuarial applications of Brownian motion, geometric Brownian motion and lognormal distribution; stochastic integrals and Ito’s formulae.

Intended learning outcomes

On successful completion of this subject, students should be able to:

  • Discuss joint and marginal distributions, analyse mixed random variables, and apply some commonly used probability distributions in insurance and finance;
  • Describe expectations and conditional expectations and apply them in solving problems in insurance and finance;
  • Apply moment generating function and probability generating functions in solving problems in insurance;
  • Describe the Laws of Large Numbers and the Central Limit Theorems and apply them to actuarial problems;
  • Solve and apply some types of ordinary differential equations in actuarial problems;
  • Apply recursive techniques in insurance and finance;
  • Apply generating transform and Laplace transform techniques in insurance;
  • State the definitions and properties of Brownian motion and geometric Brownian motion; and
  • Perform calculations with stochastic integrals and Ito’s formula.

Generic skills

On successful completion of this subject, students should have improved the following generic skills:

  • High level of development: written skills; problem solving; statistical reasoning; application of theory to practice; derivations and proofs of mathematical results

Last updated: 4 March 2025