Optimal Investment Based On The Several Types Of Utility Function

Optimal investment problem is the basis of financial economics asset pricing and risk management. Kramkov and Schachermayer (2003) showed that a necessary and sufficient condition on both, the utility function and the market.In this paper, according to the result of Kramkov and Schachermayer (2003), chose three types of utility function and give a full market model under the optimal investment, arrive at the optimal solution with individual investors and a number of investors:one Investor1.Logarithmic utility function: U(x) = In(x), optimal solution:2.Index of utility function: U(x) = - exp(-γx)γ>0,optimal solution:3.Power utility function: U(x) = (?),γ<1,γ≠0,optimal solution:two Investors1.Index of utility function:optimal solution:...