This paper solves a type of integral that is useful in approximation methods, especially in perturbation theory. This method works for a family of sums of polynomials times exponential quadratic functions. This method can be applied to economics, finance, statistics, and physics. The method uses...

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...