Optimal income drawdown and investment with longevity basis risk

We investigate a utility maximisation problem for a pension scheme which offers an income drawdown policy. Apart from market risk, we specifically focus on longevity basis risk which arises when the forces of mortality of the scheme's target population and the reference population of a longevity bond used for hedging, are not perfectly correlated. By modelling the forces of mortality of the reference and target populations as stochastic affine processes, we derive analytic solutions for the relevant investment strategy and benefit withdrawal rate. Our model also accounts for dependencies between mortality rate fluctuations and stock prices. Our extensive numerical results demonstrate that the longevity bond acts as an effective hedging instrument, even in the presence of longevity basis risk.