For annuity providers, longevity risk, i.e. the risk that future mortality trends differ from those antici-pated, constitutes an important risk factor. In order to manage this risk, new financial products, so-called longevity derivatives, may be needed, even though a first attempt to issue a longevity bond in 2004 was not successful. While different methods of how to price such securities have been proposed in recent literature, no consensus has been reached. This paper reviews, compares and comments on these different approaches. In particular, we use data from the United Kingdom to derive prices for the proposed first longevity bond and an alternative security design based on the different methods. ∗An earlier version of this paper entitled “Pricing Longevity Bonds Using Implied Survival Probabilities ” was presented at the

We study indifference pricing mechanisms for mortality contingent claims under stochas-tic mortality age structures. Our focus is on capturing the internal cross-hedge between components of an insurer’s portfolio, especially between life annuities and life insurance. We carry out an exhaustive analysis of the dynamic exponential premium principle which is the representative nonlinear pricing rule in our framework. Along the way we also derive and compare a variety of linear pricing rules which value claims under various martingale mea-sures. We illustrate our examples with realistic numerical examples that show the relative importance of model parameters.

Lessons for monetary policy: What should the consensus be? CFS Working Paper, No. 2011/13 Provided in Cooperation with:

Dedicated to my family. ii ACKNOWLEDGEMENTS This thesis would not have been possible without the support and encouragement of my Ph.D. advisors Professor Virginia Young and Professor Haitao Li. They have given me enormous freedom to pursue my own interests while providing me the right amount of guidance to ensure that my work contributes to the mainstream research in actuarial science and mathematical finance. I would like to express my gratitude to Professor Erhan Bayraktar, who taught me everything I know about probability and stochastic analysis. I wish to thank Professor Virginia Young and Professor Erhan Bayraktar for being my dissertation readers and Professor Haitao Li and Professor Kristen S. Moore for serving on my thesis committee. I owe many thanks to the Department of Mathematics, University of Michigan, for providing me the financial support during the last five years.

The Center for Financial Studies is a nonprofit research organization, supported by an association of more than 120 banks, insurance companies, industrial corporations and public institutions. Established in 1968 and closely affiliated with the University of Frankfurt, it provides a strong link between the financial community and academia. The CFS Working Paper Series presents the result of scientific research on selected topics in the field of money, banking and finance. The authors were either participants in the Center´s Research Fellow Program or members of one of the Center´s Research

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In recent years, a market for mortality derivatives began developing as a way to handle system-atic mortality risk, which is inherent in life insurance and annuity contracts. Systematic mortality risk is due to the uncertain development of future mortality intensities, or hazard rates. In this paper, we develop a theory for pricing pure endowments when hedging with a mortality forward is allowed. The hazard rate associated with the pure endowment and the reference hazard rate for the mortality forward are correlated and are modeled by diffusion processes. We price the pure endowment by assuming that the issuing company hedges its contract with the mortality forward and requires compensation for the unhedgeable part of the mortality risk in the form of a pre-specified instantaneous Sharpe ratio. The major result of this paper is that the value per contract solves a linear partial differential equation as the number of contracts approaches infinity. One can represent the limiting price as an expectation under an equivalent martingale measure. Another important result is that hedging with the mortality forward may raise or lower the price of this pure endowment comparing to its price without hedging, as determined in Bayraktar et al. [2009]. The market price of the reference mortality risk and the correlation between the two portfolios jointly determine the cost of hedging. We demonstrate our results using numerical examples.

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No-good-deal, local mean-variance and ambiguity risk pricing and hedging for an insurance payment process

For annuity providers, longevity risk, i.e. the risk that future mortality trends differ from those an-ticipated, constitutes an important risk factor. In order to manage this risk, new financial products, so-called longevity derivatives, may be needed, even though a first attempt to issue a longevity bond in 2004 was not successful. While different methods of how to price such securities have been proposed in recent literature, no consensus has been reached. This paper reviews, compares and comments on these different approaches. In particular, we use data from the United Kingdom to derive prices for the proposed first longevity bond and an alternative security design based on the different methods. Key words: longevity risk, stochastic mortality, longevity derivatives