22 citations · 29 across the 4 of their papers we have counts for
5 papers
A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for Deep BSDE solver
Akihiko Takahashi, Yoshifumi Tsuchida, Toshihiro Yamada
This paper introduces a new approximation scheme for solving high-dimensional semilinear partial differential equations (PDEs) and backward stochastic differential equations (BSDEs…
A machine learning solver for high-dimensional integrals: Solving Kolmogorov PDEs by stochastic weighted minimization and stochastic gradient descent through a high-order weak approximation scheme of SDEs with Malliavin weights
Riu Naito, Toshihiro Yamada
The paper introduces a very simple and fast computation method for high-dimensional integrals to solve high-dimensional Kolmogorov partial differential equations (PDEs). The new ma…
An Asymptotic Expansion Formula for Up-and-Out Barrier Option Price under Stochastic Volatility Model
Takashi Kato, Akihiko Takahashi, Toshihiro Yamada
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…
Strong Convergence for Euler-Maruyama and Milstein Schemes with Asymptotic Method
Hideyuki Tanaka, Toshihiro Yamada
Motivated by weak convergence results in the paper of Takahashi and Yoshida (2005), we show strong convergence for an accelerated Euler-Maruyama scheme applied to perturbed stochas…
A Semi-group Expansion for Pricing Barrier Options
Takashi Kato, Akihiko Takahashi, Toshihiro Yamada
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-D…