As the demand increases from the International Accounting Standards Board CIASB), there is correspondingly an increa..c:;ing interest in establishing a set of standard valuation approaches, which can give a clear measurement of the value of both liabilities and a..c:;sets. In the insurance industry, especially for the pensions providers and the life insurers, the importance of non-hedgable insurance risks, such as the longevity risks, is now being recognized. The appearance of insurance-linked securities provides some suitable hedging instruments to a..c:;sist the insurance r' institutions in managing these non-hedgable risk exposures. The aim of this thesis is to investigate the valuation of non-hedgable insurance risks and consider how the insurance institutions can use insura'nce-linked securities to hedge these risks. We start from a simple discrete multi-period market model. By issuing a new security, which can be viewed a..c:; an insurance liability, we are looking for the equilibrium price of the new a..c:;set. We will also use some pricing methods from financial mathematics, Le. risk minimization methods and the variance optimal martingale approach, to value the new asset.. We also introduce a set of approximate pricing methods based on power series expansions. Based on a two-factor stochastic mortality model, we simulate the price of a pension annuity. By using a linear approximation method, we bridge the gap between the discrete time model and continuous model. We extend the discrete market model to a continuous model, and we consider an investor with some future insurance liability. We use the martingale approach with a pension annuity as the numeraire and the stochastic optimal control method to find out the investor's optimal terminal wealth and the optimal trading portfolio process. By introducing a new asset, (that is, an insurance-linked security into the market model), we investigate how the investor can use the new asset to hedge the insurance risk, and how to benefit from the insurance-linked asset. We also consider some more complex asset models, such as a stochastic interest rate model, as well as a more complex and practical pension annuity model. We also investigate how the choice of a numeraire can simplify the calculation process by using a numeraire with,a general form.

This doctoral thesis investigates the sign and magnitude of a number of factor risk premia between up/bull and downlbear market movements, it assesses whether the premia of risk factors beside that of the market, also exhibit asymmetry and different signs between uplbull and down/bear markets and whether the observed behaviour of such factors is justified rationally. The factors involved in this study include the market factor, higher co-moment factors relating to coskewness and cokurtosis, and the Fama and French (1996) 8MB and HML factors. The factor risk premia are estimated using the standard two-pass Fama and MacBeth (1973) procedure, adjusted when necessary considering suggestions by subsequent researchers. This doctoral study provides new evidence and a reasoned assessment on asymmetric effects, the sign, magnitude and significance of different factor risk premia in the upturn and downturn·of the UK stock market. The study finds that the stronger beta risk and return relationship during down/bear market months is linked to inflation trends. The study reports that during downward-trending inflation months investors react asymmetrically to good and bad news. The study also finds that prospect theory is a strong candidate in explaining asymmetry between up and down market months. Further, the study estimates higher co-moments based on four different methods and finds that the coskewness premium is statistically significant in a three-moment CAPM while the premium of cokurtosis is not. Applying new methods for the first time in the UK, together with previously used ones, enables comparisons across methods and robust conclusions. This is one of the first studies to investigate higher co-moment premia during up/bull and down/bear UK markets. The study also reports symmetry between up and down market months in higher co-moment premia. However, we report that the method of estimating the third co-moment coefficient contributes to the market premium asymmetry. Furthermore, the study provides first evidence on the estimated 8MB and HML premia during up/bull and down/bear UK market months and an explanation of the observed sign and magnitude of the premia. The study shows that during up/bull and down/bear market months both size and book-to-market exhibit a relationship with returns similar ro that of beta risk. These results provide further evidence on the viability of the riskbased interpretation commonly given to 8MB and HML factors.

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