Dynamic dynamic-programming solutions for the portfolio of risky assets

Document description

Dynamic programming solutions for optimal portfolios in which the solution for the portfolio vector of risky assets is constant were solved by Merton in continuous time and by Hakansson and others in discrete time. There is no case with a closed form solution where this vector of risky asset holdings changes dynamically. This paper derives such solutions for the first time, and is thus a dynamic dynamic-programming solution as opposed to a static dynamic-programming solution for this vector. The solution is valid when there is a set of basis assets whose excess expected return is linear in the state vector, whose variance-covariance matrix is time-dependent and for which the interest rate is a quadratic function of the state vector.