distributed through time and with a risk-free asset, risky asset proportions are independent of the investor's remaining lifetime. Dynamic portfolios in continuous time With asset returns whose evolution is described by Brownian motion and which are independently and identically distributed through time, and with a risk-free asset, one can obtain an explicit solution for the demand for the unique optimal mutual fund, and that demand is linear in initial wealth. References External links Closed form solution for a consumption savings problem with HARA utility Financial risk modeling Expected utility Utility function types