Wydawnictwa / Banach Center Publications / Wszystkie tomy

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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.