22 citations · 38 across the 17 of their papers we have counts for
22 papers
New asymptotic expansion formula via Malliavin calculus and its application to rough differential equation driven by fractional Brownian motion
Akihiko Takahashi, Toshihiro Yamada
This paper presents a novel generic asymptotic expansion formula of expectations of multidimensional Wiener functionals through a Malliavin calculus technique. The uniform estimate…
Equilibrium Price Formation with a Major Player and its Mean Field Limit
Masaaki Fujii, Akihiko Takahashi
In this article, we consider the problem of equilibrium price formation in an incomplete securities market consisting of one major financial firm and a large number of minor firms.…
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…
Strong Convergence to the Mean-Field Limit of A Finite Agent Equilibrium
Masaaki Fujii, Akihiko Takahashi
We study an equilibrium-based continuous asset pricing problem for the securities market. In the previous work [16], we have shown that a certain price process, which is given by t…
A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition
Masaaki Fujii, Akihiko Takahashi
In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purch…
Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs
Masaaki Fujii, Akihiko Takahashi, Masayuki Takahashi
We demonstrate that the use of asymptotic expansion as prior knowledge in the "deep BSDE solver", which is a deep learning method for high dimensional BSDEs proposed by Weinan E, H…
Anticipated Backward SDEs with Jumps and quadratic-exponential growth drivers
Masaaki Fujii, Akihiko Takahashi
In this paper, we study a class of Anticipated Backward Stochastic Differential Equations (ABSDE) with jumps. The solution of the ABSDE is a triple where is a semimar…
Solving Backward Stochastic Differential Equations with quadratic-growth drivers by Connecting the Short-term Expansions
Masaaki Fujii, Akihiko Takahashi
This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of semi-analytic asymptotic expansions applied to short-ti…
Quadratic-exponential growth BSDEs with Jumps and their Malliavin's Differentiability
Masaaki Fujii, Akihiko Takahashi
We investigate a class of quadratic-exponential growth BSDEs with jumps. The quadratic structure introduced by Barrieu & El Karoui (2013) yields the universal bounds on the possibl…
Asymptotic Expansion for Forward-Backward SDEs with Jumps
Masaaki Fujii, Akihiko Takahashi
This work provides a semi-analytic approximation method for decoupled forwardbackward SDEs (FBSDEs) with jumps. In particular, we construct an asymptotic expansion method for FBSDE…
A General Framework for the Benchmark pricing in a Fully Collateralized Market
Masaaki Fujii, Akihiko Takahashi
Collateralization with daily margining has become a new standard in the post-crisis market. Although there appeared vast literature on a so-called multi-curve framework, a complete…
Optimal Hedging for Fund & Insurance Managers with Partially Observable Investment Flows
Masaaki Fujii, Akihiko Takahashi
All the financial practitioners are working in incomplete markets full of unhedgeable risk-factors. Making the situation worse, they are only equipped with the imperfect informatio…
Making Mean-Variance Hedging Implementable in a Partially Observable Market
Masaaki Fujii, Akihiko Takahashi
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 process…
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…
An FBSDE Approach to American Option Pricing with an Interacting Particle Method
Masaaki Fujii, Seisho Sato, Akihiko Takahashi
In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The well-known decomposition…
Perturbative Expansion Technique for Non-linear FBSDEs with Interacting Particle Method
Masaaki Fujii, Akihiko Takahashi
In this paper, we propose an efficient Monte Carlo implementation of non-linear FBSDEs as a system of interacting particles inspired by the ideas of branching diffusion method. It…
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…
Perturbative Expansion of FBSDE in an Incomplete Market with Stochastic Volatility
Masaaki Fujii, Akihiko Takahashi
In this work, we apply our newly proposed perturbative expansion technique to a quadratic growth FBSDE appearing in an incomplete market with stochastic volatility that is not perf…
Clean Valuation Framework for the USD Silo
Masaaki Fujii, Akihiko Takahashi
In the forthcoming ISDA Standard Credit Support Annex (SCSA), the trades denominated in non-G5 currencies as well as those include multiple currencies are expected to be allocated…
Analytical Approximation for Non-linear FBSDEs with Perturbation Scheme
Masaaki Fujii, Akihiko Takahashi
In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed wi…
Collateralized CDS and Default Dependence
Masaaki Fujii, Akihiko Takahashi
In this paper, we have studied the pricing of a continuously collateralized CDS. We have made use of the "survival measure" to derive the pricing formula in a straightforward way.…
Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA
Masaaki Fujii, Akihiko Takahashi
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 collate…