For an investor with constant absolute risk aversion, we informally derive the first‐order asymptotics of the optimal investment strategy as the bid‐ask spread becomes small. For general It\^o processes, the first order correction term is expressed in terms of the quadratic variation of the frictionless optimizer. This result allows to quantify the impact of, e.g., predictability and stochastic volatility on portfolio choice in the presence of transaction costs. Applied to an investor holding a random endowment, it also leads to a generalization of the asymptotic utility‐based hedging strategies determined by Whalley and Wilmott (1997) for a constant opportunity set.
This is joint work with Jan Kallsen.