When solving the Heston model using affine reduction to a system of ODE, which is established practice (AndersonPiterbarg-MomentExplosions2007, SmallTimeSmileTermStructureImpliedVolHeston-2012) with notation
$\langle dW^1_t,dW^2_t \rangle= \rho dt$
One notes that the the parabolic equation determined by the model can be solved using the ansatz by a system of ordinary differential equations
and the latter Riccati equation can have explosion in finite time. So what happens when we replace in (*) with a fractional Brownian motion? Essentially and not at all rigorously for the moment, and where .