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.
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