A portfolio choice problem under risk capacity constraint

This paper studies the asset allocation problem for a retiree facing longevity risk and living standard risk. We introduce a risk capacity constraint to reduce the living standard risk in the retirement period. Whether the retiree focuses on intertemporal consumption or inheritance wealth, we demonstrate a unique number to measure the expected lump sum of the spending post-retirement. The optimal portfolio is nearly neutral to the stock market movement if the portfolio’s value is higher than this critical value; otherwise, the retiree actively invests in the stock market. As a comparison, we consider a dynamic leverage constraint and show that the corresponding optimal portfolio would lose significantly in stressed markets.