2008 Symposium

The 2008 UNSW Actuarial Symposium was held on 31 October 2008 at the UNSW Australia Business School.

The following presentations were made:

Dr Greg Taylor Taylor-Fry Consulting Actuaries - Professorial Visiting Fellow, Actuarial Studies, UNSW: A Simple Model of Insurance Market Dynamics

The purpose of the presentation is to construct and study a simple but realistic model of an insurance market. The model has a minimalist construction in the sense that the number of parameters defining it is strictly limited and the elimination of any one of them would destroy its realism.

There are, in fact, 11 essential parameters. Each of the parameters has a physical interpretation. Some determine competitive effects within the market, some barriers to entry, and so on. The effect of each on various aspects of the market is examined in the presence of simulated loss experience. The aspects of the market considered include stability of premium rates, profitability, market concentration, and others.

Some of the parameters are capable of use as regulatory controls. Two parameters, in addition to the original 11, are explicit price controls. Despite its simplicity, the model displays considerably complex behaviour. Some results are intuitive but some are not. For this reason, regulatory controls need to be applied with great caution lest they induce perverse effects, possibly even the reverse of those intended.

The effect of the parameters on market behaviour is first studied in the absence of catastrophic events from the loss experience. Subsequently, the effect of a single such event is studied.

Dr Benjamin Avanzi: On Optimal Dividend Strategies: Review and Dual Model

In his seminal paper, Bruno de Finetti (1957) laid the foundations of what would become an increasingly popular branch of risk theory: the study of dividend strategies. The recent burst of research in this field encouraged us to carry out a systematic literature review of modern collective risk theory with dividend strategies. The first paper that is presented aims at a taxonomical synthesis of the 50 years of research that followed de Finetti's original paper.

The second part of the presentation is dedicated to the dual model. In this model, the surplus of a company is a Levy process with sample paths that are skip-free downwards. The aggregate gains process is the sum of a shifted compound Poisson process and an independent Wiener process. By means of Laplace transforms, it is shown how the expectation of the discounted dividends until ruin can be calculated, if a barrier strategy is applied, and how the optimal dividend barrier can be determined. Conditions for optimality are discussed and several numerical illustrations are given.

Dr Bernard Wong: On Modelling Long Term Stock Returns with Ergodic Diffusion Processes - Arbitrage and Arbitrage-Free Specifications

We investigate the arbitrage-free property of stock price models where the local martingale component is based on an ergodic diffusion with a specified stationary distribution. These models are particularly useful for insurer asset-liability management as they allow the modelling of long term stock returns with heavy tailed ergodic diffusions, with tractable, time homogeneous dynamics, and which moreover admit a complete financial market.

Unfortunately the standard specification of these models in the literature admit arbitrage opportunities. We investigate in detail the features of the existing model specifications which create these arbitrage opportunities, and consequently construct a modification that is arbitrage free.

Dr Changki Kim joint with Taehan Bae: Motor Insurance Loss Rate Options and Swaps

In an attempt to manage the risk of mismatch between the actual claims and the anticipated claim amounts in motor insurance pool we introduce a few new concepts of motor loss rate-linked securities such as motor loss rate swaps and motor loss rate options.

These securities can transfer the motor insurance loss rate risks to the capital markets. For the valuation of motor loss rate-linked securities we assume that motor insurance aggregate claims follow Compound Poisson distribution. Esscher transform is chosen for a risk adjusted measure change.

We use the Fourier transform of the risk neutral distribution of increment of loss process and derive an integral expression of the price of a path-dependent Bermudan option on the motor loss rate. Also the price formula of a motor loss rate cap is given. As a simple example we consider a fixed-for-floating plain vanilla motor loss rate swap and obtain an explicit formula for the motor loss rate swap price. We show some numerical examples under a few specified assumptions on the distribution of the discounted losses and the parameters.

Carolyn Ndigwako King'ori and Professor Michael Sherris: Econometric Analysis of Mortality - Trends, Volatility, Unit Roots, and Cross Country Comparison using Co-integration

The modelling of trends and volatility for mortality improvement has attracted increased attention driven by ageing populations around the world and the significant financial implications. The Lee-Carter model was based on the level of mortality and a single improvement factor with differential impacts by age.

Financial models that allow for the incorporation of a price of risk have attracted more recent attention along with multiple factor models. Despite this level of research, there has been limited analysis as to whether mortality has deterministic long run trends (trend stationary) or stochastic trends (unit roots) and limited research into common trends across countries.

The number of factors driving mortality change has not been systematically investigated at a macro country level. This paper investigates trends, including common trends through co-integration, and volatility of mortality in a number of developed countries including Australia, England, Japan, Norway and USA. Principal components analysis is used to assess the number of factors driving mortality changes and factors such as GDP, health expenditures are examined as possible factors.

Dr Sachi Purcal joint with Samuel Fung: Optimal Lifetime Financial Behaviour and the Question of Housing

We consider the optimum consumption behaviour of a utility maximising consumer over her lifetime. Our model includes financial considerations: how much to invest in safe assets, risky assets, as well as how much life insurance and annuities to buy? Finally, we model housing purchase and how this asset, with its non-perishable characteristics, affects behaviour.

Jack Jie Ding joint with Prof Michael Sherris: Modelling and Hedging CDO Tranche Spread Risks

The Gaussian copula model has become a standard model for pricing CDOs. There are many extensions of this model to allow for its shortcomings, but very few of them are able to provide a robust basis for hedging. In this paper we discuss the issues of hedging synthetic CDO tranche spread risks with the traded market index contracts.

In order to assess a model for hedging purposes it should at least be able to correctly price future CDO tranches conditional on the future CDO index spread. This is also closely related to the ability of the model to price CDOs on non-standard portfolios based on the spread of the traded index contracts on the portfolio.

Currently the market computes a tranche's delta to the index spread by assuming the tranche correlation is constant. Based on the observation that estimated default correlations and the default probabilities determined from market data for CDOs are highly correlated, extensions of the market standard Gaussian copula model are considered including fitting the base correlation curve as a function of the default probability as well as using an implied copula model where the default correlation is a function of the default probability.

The models assessed are calibrated to the traded CDO index spread and then compared based on the mean absolute pricing error (between actual and predicted CDO tranche spreads) for the different models.