This paper provides the optimal position management strategy for a market maker who has to face uncertain customer orders in an "illiquid" market, where the market maker's continuous trading through a traditional exchange incurs stochastic linear price impacts. In addition, it is supposed that...

This paper develops an asymptotic expansion technique in momentum space for stochastic filtering. It is shown that Fourier transformation combined with a polynomial-function approximation of the nonlinear terms gives a closed recursive system of ordinary differential equations (ODEs) for the...

This paper derives a new semi closed-form approximation formula for pricing an up-and-out barrier option under a certain type of stochastic volatility model including SABR model by applying a rigorous asymptotic expansion method developed by Kato, Takahashi and Yamada (2012). We also demonstrate...

This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develops a semi-group expansion scheme for the Cauchy-Dirichlet problem in the second-order parabolic partial differential equations (PDEs) arising in barrier option...

　　 A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed. The perturbation parameter "∈" is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard <em>small-diffusion</em> asymptotic expansion method, the dynamics of...

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...

A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed. The perturbation parameter "ε" is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion method, the dynamics of variables given by the...

This paper provides the optimal position management strategy for a market maker who has to face uncertain customer orders in an "illiquid" market, where the market maker’s continuous trading through a traditional exchange incurs stochastic linear price impacts. In addition, it is supposed...