Dynamic Asset Allocation: Portfolio Decomposition Formula and Applications

A new decomposition of the optimal portfolio, in dynamic models with von Neumann-Morgenstern preferences and Ito prices, is established. The formula rests on a change of numeraire that uses pure discount bonds as units of account. The dynamic hedging demand has two components. The first hedge insures against fluctuations in an optimally designed bond with a maturity date matching the investor's horizon. The second hedge immunizes against fluctuations in the market price of risk in the bond numeraire. Various applications are examined. New results concerning the behavior of extremely risk-averse individuals, the demand for bonds and its long-horizon limit, and the optimal portfolio in incomplete markets are derived.