Non†myopic portfolio choice with unpredictable returns: The jump†to†default case

If a risky asset is subject to a jump†to†default event, the investment horizon affects the optimal portfolio rule, even if the asset returns are unpredictable. The optimal rule solves a non†linear differential equation that, by not depending on the investor's pre†default value function, allows for its direct computation. Importantly for financial planners offering portfolio advice for the long term, tiny amounts of constant jump†to†default risk induce marked time variation in the optimal portfolios of long†run conservative investors. Our results are robust to the introduction of multiple non†defaultable risky assets.