Optimal portfolio choice in the bond market (Q881421)

The authors consider the problem of optimal portfolio choice when the traded instruments are the set of zero-coupon bonds. They specify a general Heath-Jarrow-Morton model of the infinite-dimensional dynamics of the bond prices. They fix a utility function and a planning horizon, consider a functional of the accumulated wealth generated by the self-financing trading strategy and characterize the strategy that maximizes this functional. It is supposed that the driving Wiener process is infinite-dimensional and the bond prices are Markovian. Using the Clark-Ocone formula and convex duality, sufficient conditions are given for the existence of an optimal trading strategy. It is proved that the optimal portfolio naturally decomposes as a sum of three mutual funds. The description of these funds is presented. Then the optimal portfolio is examined in detail for a class of Gaussian random fields models.