Longevity-linked securities pricing

Reinsurance contracts, particularly those linked to longevity, are crucial for insurance companies seeking to transfer mortality and longevity risk to third parties. Despite their importance, these contracts lack a standardized pricing approach due to the incomplete market in which they are traded. Traditional methods, such as risk-neutral pricing, are inadequate because the cash flows from reinsurance contracts cannot be replicated in open markets. This study introduces utility indifference pricing as a solution, positing that the price of a contract should equal the premium at which the market maker is indifferent between selling and not selling the contract, in terms of maximized expected utility. By employing numerical optimization and deep learning to facilitate the utility indifference pricing, this research develops a robust framework for pricing a longevity-linked security. Moreover, a non-universal risk-neutral measure is found to be a good approximation of the utility indifference pricing method. This thesis represents stocks and survival rates as binomial trees, facilitating dynamic programming techniques for optimization. The findings address the limitations of previous methods and investigate how the optimal asset allocation decision and utility indifference price react in terms of the longevity risk. This dual perspective enhances the theoretical foundation and practical application of pricing in incomplete markets, offering significant contributions to the field of financial risk management.