Optimal investment problem with M-CEV model: closed form solution and applications to the algorithmic trading

This paper studies an optimal investment problem under M-CEV with power utility function. Using Laplace transform we obtain explicit expression for optimal strategy in terms of confluent hypergeometric functions. For obtained representations we derive asymptotic and approximation formulas contains only elementary functions and continued fractions. These formulas allow to make analysis of impact of models parameters and effects of parameters misspecification. In addition we propose some extensions of obtained results that can be applicable for algorithmic strategies.