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

## TL;DR

This paper derives explicit solutions for an optimal investment problem under the M-CEV model using Laplace transforms, providing formulas for strategy analysis and extensions for algorithmic trading applications.

## Contribution

It presents a closed-form solution for the M-CEV model's optimal investment problem and develops elementary and continued fraction approximations for practical analysis.

## Key findings

- Explicit optimal strategy expressions using hypergeometric functions
- Asymptotic and approximation formulas for parameter analysis
- Extensions applicable to algorithmic trading strategies

## Abstract

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 model's parameters and effects of parameters misspecification. In addition we propose some extensions of obtained results that can be applicable for algorithmic strategies.