  We study the Merton problem of optimal consumption-investment for the case of
two investors sharing a final wealth. The typical example would be a husband
and wife sharing a portfolio looking to optimize the expected utility of
consumption and final wealth. Each agent has different utility function and
discount factor. An explicit formulation for the optimal consumptions and
portfolio can be obtained in the case of a complete market. The problem is
shown to be equivalent to maximizing three different utilities separately with
separate initial wealths. We study a numerical example where the market price
of risk is assumed to be mean reverting, and provide insights on the influence
of risk aversion or discount rates on the initial optimal allocation.
