Financial Value of Information in Complete Market Models

Abstract

This paper deals with the problem of the cost of uncertainty associated with the utility maximization problem in a complete market with multiple risky assets and unobservable dividends. This leads naturally to a partial information setup from which filtering techniques can be applied. Using a distortion power solution for the primal problem, we prove that the value function can be expressed in terms of the solution of a semilin- ear PDE, which is suggested by the dynamic programming approach. An explicit solution is obtained for HARA utilities, which we treat in a unified manner. Under these general results, the links between both the optimal investment strategy and the value function under full and partial informa- tion are explicited. This allows then to draw some insights on the financial value of information: the minimal initial endowment an investor with partial information must hold in order to attain the same expected utility as under full information. We apply our approach to a two-assets market model and discuss the numerical results in terms of optimal investment strategy.