Pacific Institute for the Mathematical Sciences - PIMS

This paper establishes a new decomposition of the optimal portfolio
policy in dynamic asset allocation models with arbitrary vNM
preferences and Ito prices. The formula rests on a change of
num'{e}raire which consists in taking pure discount bonds as units of
account. When expressed in this new num'{e}raire the dynamic hedging
demand is shown to have two components. If the individual cares solely
about terminal wealth, the first hedge insures against fluctuations in
a long term bond with maturity date matching the investor's horizon and
face value determined by bequest preferences. The second hedge
immunizes against fluctuations in future bond return
volatilities and market prices of risk. When the individual also cares
about intermediate consumption the first hedging component becomes a
coupon-paying bond with coupon payments tailored to the consumption
needs. The decomposition formula is used to examine the existence of
preferred habitats, the investment behavior of extremely risk averse
individuals, the demand for long term bonds, the optimal international
asset allocation rule, the preference for I-bonds in inflationary
environments and the integration of fixed income management and asset
allocation.

MITACS Math Finance Seminar 2006