6 citations · 14 across the 6 of their papers we have counts for
7 papers
Third-moment cancellation and predictable representation in finite-state BSDE approximation
Akihiro Tanaka
We study finite-state approximations of Brownian-driven Markovian backward stochastic differential equations when the same one-step increment is used both for weak propagation and…
Notes on Backward Stochastic Differential Equations for Computing XVA
Jun Sekine, Akihiro Tanaka
The X-valuation adjustment (XVA) problem, which is a recent topic in mathematical finance, is considered and analyzed. First, the basic properties of backward stochastic differenti…
-error estimates for approximation of irregular functionals of random vectors
Dai Taguchi, Akihiro Tanaka, Tomooki Yuasa
Avikainen showed that, for any , and any function of bounded variation in , it holds that $\mathbb{E}[|f(X)-f(\widehat{X})|^{q}] \leq C(p,q) \ma…
Polyhedral approximations of the semidefinite cone and their application
Yuzhu Wang, Akihiro Tanaka, Akiko Yoshise
We develop techniques to construct a series of sparse polyhedral approximations of the semidefinite cone. Motivated by the semidefinite (SD) bases proposed by Tanaka and Yoshise (2…
On the Euler--Maruyama scheme for degenerate stochastic differential equations with non-sticky condition
Dai Taguchi, Akihiro Tanaka
The aim of this paper is to study weak and strong convergence of the Euler--Maruyama scheme for a solution of one-dimensional degenerate stochastic differential equation $\mathrm{d…
Probability density function of SDEs with unbounded and path--dependent drift coefficient
Dai Taguchi, Akihiro Tanaka
In this paper, we first prove that the existence of a solution of SDEs under the assumptions that the drift coefficient is of linear growth and path--dependent, and diffusion coeff…
LP-based Tractable Subcones of the Semidefinite Plus Nonnegative Cone
Akihiro Tanaka, Akiko Yoshise
The authors in a previous paper devised certain subcones of the semidefinite plus nonnegative cone and showed that satisfaction of the requirements for membership of those subcones…