Dimension reduction and Mutual Fund Theorem in maximin setting for bond market

Abstract

We study optimal investment problem for a continuous time stochasticmarket model. The risk-free rate, the appreciation rates, and thevolatility of the stocks are all random; they are not necessaryadapted to the driving Brownian motion, their distributions areunknown, and they are supposed to be currently observable. To coverfixed income management problems, we assume that the number of riskyassets can be larger than the number of driving Brownian motion. Theoptimal investment problem is stated as a problem with a {\itmaximin} performance criterion to ensure that a strategy is foundsuch that the minimum of expected utility over all possibleparameters is maximal. We show that Mutual Fund Theorem holds forthis setting. We found also that a saddle point exists and can befound via minimization over a single scalar parameter.