This paper presents an extension of a general computational scheme for asymptotic expansions proposed in earlier works by the authors and coworkers. In the earlier works, a new method was developed for the computation of an arbitrary-order expansion with a normal benchmark distribution in a...

The mean-variance hedging (MVH) problem is studied in a partially observable market where the drift processes can only be inferred through the observation of asset or index processes. Although most of the literatures treat the MVH problem by the duality method, here we study a system consisting...

This paper provides a survey on an asymptotic expansion approach to valuation and hedging problems in nance. The asymptotic expansion is a widely applicable methodology for analytical approximations of expectations of certain Wiener functionals. Hence not only academic researchers but also...

In this paper, we propose an efficient Monte Carlo implementation of a non-linear FBSDE as a system of interacting particles inspired by the idea of the branching diffusion method of McKean. It will be particularly useful to investigate large and complex systems, and hence it is a good...

This paper develops a new efficient scheme for approximations of expectations of the solutions to stochastic differential equations (SDEs). In particular, we present a method for connecting approximate operators based on an asymptotic expansion with multidimensional Malliavin weights to compute...

This paper proposes a general approximation method for the solution to a second-order parabolic partial differential equation(PDE) widely used in finance through an extension of Leandre's approach (Leandre (2006,2008)) and the Bismut identiy(e.g. chapter IX-7 of Malliavin (1997)) in Malliavin...

This paper presents a new computational scheme for an asymptotic expansion method of an arbitrary order. The asymptotic expansion method in finance initiated by Kunitomo and Takahashi [1992], Yoshida [1992b] and Takahashi [1995], [1999] is a widely applicable methodology for an analytic...

In this work, we have presented a simple analytical approximation scheme for the generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out recursive...

The importance of collateralization through the change of funding cost is now well recognized among practitioners. In this article, we have extended the previous studies of collateralized derivative pricing to more generic situation, that is asymmetric and imperfect collateralization as well as...