SOLVING THE FRACTIONAL DIFFERENTIAL RICCATI EQUATION ARISING FROM THE HESTON MODEL WITH NEURAL NETWORKS AND POWER SERIES EXPANSION

In my work I explore the fractional differential Riccati equation, which is a particular equation that arises in many different mathematical problems. In particular, It arises in the financial stochastic model of Heston, more precisely, the rough Heston model. Solving the fractional Riccati allows us to express the characteristic function of the rough Heston and then perform pricing of call options. Solving the fractional differential Riccati equation is not simple task. In my work I explore one method using fractional power series expansion from the work of Callegaro G. and then I try something new with neural networks. The attempts with neural networks sometimes work good and sometimes not. The idea of solving that has been mostly an independent exploration, with inspiration from works solving standard differential equations.