We develop a general approach to portfolio optimization in futures markets. Following the Heath–Jarrow–Morton (HJM) approach, we model the entire futures price curve at once as a solution of a stochastic partial differential equation. We also develop a general formalism to handle portfolios...

A stochastic partial differential equation, or SPDE, describes the dynamics of a stochastic process defined on a space-time continuum. This paper provides a new method for solving SPDEs based on the method of lines (MOL). MOL is a technique that has largely been used for numerically solving...

In this paper, we establish an equivalence relationship between the wellposedness of forward–backward SDEs (FBSDEs) with random coefficients and that of backward stochastic PDEs (BSPDEs). Using the notion of the “decoupling random field”, originally observed in the well-known Four Step...

We show an averaging result for a system of stochastic evolution equations of parabolic type with slow and fast time scales. We derive explicit bounds for the approximation error with respect to the small parameter defining the fast time scale. We prove that the slow component of the solution of...

In this paper we study some linear and quasi-linear stochastic equations with the random fractional Laplacian operator driven by arbitrary Lévy processes. The driving noise can be space–time in the case of one dimensional spacial variable. We prove uniqueness and existence of such equations...