  We consider a time-consistent mean-variance portfolio selection problem of an
insurer and allow for the incorporation of basis (mortality) risk. The optimal
solution is identified with a Nash subgame perfect equilibrium. We characterize
an optimal strategy as solution of a system of partial integro-differential
equations (PIDEs), a so called extended Hamilton-Jacobi-Bellman (HJB) system.
We prove that the equilibrium is necessarily a solution of the extended HJB
system. Under certain conditions we obtain an explicit solution to the extended
HJB system and provide the optimal trading strategies in closed-form. A
simulation shows that the previously found strategies yield payoffs whose
expectations and variances are robust regarding the distribution of jump sizes
of the stock. The same phenomenon is observed when the variance is correctly
estimated, but erroneously ascribed to the diffusion components solely.
Further, we show that differences in the insurance horizon and the time to
maturity of a longevity asset do not add to the variance of the terminal
wealth.
