Risk minimizing strategies for a portfolio of interest-rate securities
The paper presents an application of stochastic control methods to fixed income management in an incomplete market with external economic factors. The objective of an investor is the minimization of a shortfall risk. The problem is reduced to the multidimensional Bellman equation. It is shown that for a large class of loss functions the equation possesses a continuous solution. We also consider loss functions from the HARA class and prove that for such functions the Hamilton-Jacobi-Bellman equation has a sufficiently smooth solution. This solution guarantees the existence of a well defined investment strategy. A special example of the bond portfolio with interest rates governed by the Gaussian HJM model is solved explicitly.