Optimal investment in a market with borrowing and quadratic-affine interest rates

Abstract

We consider the problem of optimal investment in a market with borrowing and stochastic interest rates. We assume a quadratic-affine model for the bond rate which includes the Hull-White and Cox-Ingersoll-Ross models as special cases. Due to borrowing, this is an optimal stochastic control problem with nonlinear system dynamics. An explicit closed-form solution is found for the case of a power and logarithmic utility from terminal wealth as a linear state-feedback control.