A new method for analysing and projecting mortality is proposed and examined. The method takes observed time series of survival probabilities, finds the corresponding z-scores in the standard normal distribution and forecasts the z-scores. The z-scores appear to follow a common simple linear progression in time and hence forecasting is straightforward. Analysis on the z-score scale offers useful insights into the way mortality evolves over time. The method and extensions are applied to Australian female mortality data to derive projections to the year 2100 in both survival probabilities and expectations of life.

The Capital Asset Pricing Model arises in an economy where agents have exponential utility functions and aggregate consumption is normally distributed, and gives the prices of assets with payoffs which are jointly normal with consumption. Such assets have normal marginal distributions and have dependence with consumption characterised by a normal copula. Wang has derived a transform which extends the CAPM by allowing pricing of assets in such an economy which have non-normal marginal distributions but still are normal-copula with consumption.

Here we set out the stochastic discount factors corresponding to this version of the CAPM and to Wang’s transform, and show how to calculate stochastic discount factors and hence asset prices for assets whose dependence with consumption is non-normal. We show that the impact of dependency structure on asset prices is significant.

In this paper the dynamic portfolio selection problem is studied for the first time in a dual utility theory framework. The Wang transform is used as distortion function and well diversified optimal portfolios result both with and without short sales allowed.

This paper proposes a multivariate extension of the equilibrium pricing transforms for pricing general financial and insurance risks. The multivariate Esscher and Wang transforms are derived from Bühlmann’s equilibrium pricing model (1980) under some assumptions on the aggregate risk. It is shown that the Esscher and Wang transforms coincide with each other when the underlying risks are normally distributed.

In this paper we revisit an economic model of Buhlmann (ASTIN Bulletin, 1980) and derive equilibrium pricing transforms. We obtain the Esscher Transform and the Wang Transform under different sets of assumptions on the aggregate economic environment. We show that the Esscher Transform and the Wang Transform exhibit very different behaviors when used in pricing insurance risks.