Notes and Comments: Sup-convolutions of HARA utilities in the affine term structure

In the financial literature, the problem of maximizing the expected utility of the terminal wealth has been investigated extensively (for a survey, see, e.g., Karatzas and Shreve (1998), p. 153, and references therein) by using different approaches. In this paper, we extend the existing literature in two directions. First, we let the utility function U(.) of the financial agent (who is a price taker) be implicitly defined through I(.)=(U ′ (.))–1, which is assumed to be additively separable, i.e., I(.)=∑ k=1 N I k (.). Second, we solve the investment problem in the general affine term structure model proposed by Duffie and Kan (1996) in which the functions I k (.), k=1,...,N are associated to HARA utility functions (with possibly different risk aversion parameters), and we show that the utility maximization problem leads to a Riccati ODE. Moreover, we extend to the multi-factor framework the stability result proved in Grasselli (2003), namely, the almost-sure convergence of the solution with respect to the parameters of the utility function. Mathematics Subject Classification (2000): 91B28 Journal of Economic Literature Classification: G11