Practical partial equilibrium framework for pricing of mortality-linked instruments in continuous time

This work considers a partial equilibrium approach for pricing longevity bonds in a stochastic mortality intensity setting. Thus, the pricing methodology developed in this work is based on a foundational economic principle and is realistic for the currently illiquid life market. Our model consists of economic agents who trade in risky financial security and longevity bonds to maximize the monetary utilities of their trades and income. Stochastic mortality intensity affects agents' income, resulting in market incompleteness. The longevity bond introduced acts as a hedge against mortality risk, and we prove that it completes the market. From a practical perspective, we characterize and compute the endogenous equilibrium bond price. In a realistic setting with two agents in a transaction, numerical experiments confirm the expected intuition of price dependence of model parameters.