Existence of Lévy term structure models (Q928496)

The authors consider Lévy term structure model for the forward rate process that includes stochastic volatility process. This leads to infinite-dimensional equation that is not simply a system of infinitely many univariate stochastic equations but involve complicated functional dependence. The existence and in some special cases the uniqueness proof for the Lévy case of the mentioned above version of Heath-Jarrow-Morton-Musiela equation is provided for various choices of the state Hilbert space \(H\). The existence result is based on a general result for Hibert space valued stochastic equations. The càdlág property of the solution is discussed as it is important for financial applications.