Canonical Markovian representations of stochastic Volterra equations

We introduce canonical Markovian representations of stochastic Volterra processes in terms of transport stochastic partial differential equations (SPDEs). Solution theories are equivalent but the Markovian representation... [ view full abstract ]

We introduce canonical Markovian representations of stochastic Volterra processes in terms of transport stochastic partial differential equations (SPDEs). Solution theories are equivalent but the Markovian representation allows for novel numerical techniques as well as solution concepts that are hard to guess from the Volterra equations' point of view. If the instantaneous characteristics of the Volterra process are affine or polynomial the Markovian lift is affine or polynomial as well, providing another explanation of certain affine or polynomial techniques present in the Volterra world. Examples from rough volatility modeling are included.