Portfolio choice with time horizon risk

I study the allocation problem of investors who hold their portfolio until a target wealth is attained. The strategy suppresses final wealth uncertainty but creates an investment  time horizon risk. I begin with a simple mean variance model transposed in the duration domain, then study a dynamic portfolio choice problem with Generalized Expected Discounted Utility preferences. Using long-term US return data, I show in the mean variance model that a large amount of  time horizon risk can be diversified away by investing a significant share of equities. In the dynamic model, more impatient investors are also more averse to timing risk and invest less in equities. The equity share is downward trending with accumulated wealth relative to its target.