# Masaaki FujiiThe University of Tokyo | Todai · Department of Economics

Masaaki Fujii

Ph.D. Physics & Ph.D. Economics

## About

84

Publications

15,067

Reads

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1,793

Citations

Introduction

Additional affiliations

April 2011 - July 2018

April 2004 - December 2008

**Morgan Staneley Securities, Ltd**

Position

- Vice President

April 2002 - October 2002

Education

April 2009 - March 2013

April 1999 - March 2004

## Publications

Publications (84)

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 possible solutions. With local Lipschitz continuity and the so-called AΓ-condition for the comparison principle to hold, we prove the existence of a unique solution under the ge...

We study an equilibrium-based continuous asset pricing problem for the securities market. In the previous work [M. Fujii and A. Takahashi (2022), SIAM J. Control Optim., 60, pp. 259--279], we have shown that a certain price process, which is given by the solution to a forward-backward stochastic differential equation of conditional McKean--Vlasov t...

In this work, we develop an equilibrium model for price formation of securities in a market composed of two populations of different types: the first one consists of cooperative agents, while the other one consists of non-cooperative agents. The trading of every cooperative member is assumed to be coordinated by a central planner. In the large popu...

This paper presents an asset pricing model in an incomplete market involving a large number of heterogeneous agents based on the mean field game theory. In the model, we incorporate habit formation in consumption preferences, which has been widely used to explain various phenomena in financial economics. In order to characterize the market-clearing...

In this paper, we study a problem of equilibrium price formation among many investors with exponential utility. The investors are heterogeneous in their initial wealth, risk-averseness parameter, as well as stochastic liability at the terminal time. We characterize the equilibrium risk-premium process of the risky stocks in terms of the solution to...

In this work, we develop an equilibrium model for price formation of securities in a market composed of two populations of different types: the first one consists of cooperative agents, while the other one consists of non-cooperative agents. The trading of every cooperative member is assumed to be coordinated by a central planner. In the large popu...

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. They carry out continuous trading via the securities exchange to minimize their cost while facing idiosyncratic and common noises as well as stochastic order flows from...

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. They carry out continuous trading via the securities exchange to minimize their cost while facing idiosyncratic and common noises as well as stochastic order flows from...

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 the solution to a forward backward stochastic differential equation of conditional McKean-
Vlasov type, asymptotically clears the market in the large population limit. In...

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-purchase orders in the exchange market, where a large number of agents 1 ≤ i ≤ N are interacting through the market price. Adopting a mean field game (MFG) approach, we find a...

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from Pontryagin's stochastic maximum principle. Although the same cost functions as well as the coefficient functions...

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 et al. (Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations, 2017b. arXiv:1706....

This work provides a semi-analytic approximation method for decoupled forward-backward SDEs (FBSDEs) with jumps. In particular, we construct an asymptotic expansion method for FBSDEs driven by the random Poisson measures with σ-finite compensators as well as the standard Brownian motions around the small-variance limit of the forward SDE. We provid...

In this paper, we study a class of Anticipated Backward Stochastic Differential Equations (ABSDE) with jumps. The solution of the ABSDE is a triple (Y,Z,ψ) where Y is a semimartingale, and (Z,ψ) are the diffusion and jump coefficients. We allow the driver of the ABSDE to have linear growth on the uniform norm of Y's future paths, as well as quadrat...

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-time intervals. Although there remains a condition which needs to be checked a posteriori, one can avoid altogether time-consuming Monte Carlo simulation and other numerica...

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, Han & Jentzen (2017), drastically reduces the loss function and accelerates
the speed of convergence. We illustrate the technique and its implications by Bergman’s
model w...

In this paper, we study a class of Anticipated Backward Stochastic Differential Equations (ABSDE) with jumps. The solution of the ABSDE is a triple $(Y,Z,\psi)$ where $Y$ is a semimartingale, and $(Z,\psi)$ are the diffusion and jump coefficients. We allow the driver of the ABSDE to have linear growth on the uniform norm of $Y$'s future paths, as w...

Collateralization with daily margining has become a new standard in the post-crisismarket. Although there appeared vast literature on a so-called multi-curve framework, a complete picture of a multi-currency setup with cross-currency basis can be rarely found since our initial attempts. This work gives its extension regarding a general framework of...

In this article, we propose a new numerical computation scheme for Markovian backward stochastic differential equations (BSDEs) by connecting the semi-analytic short-term approximation applied to each time interval, which has a very simple form to implement. We give the error analysis for BSDEs which have generators of quadratic growth with respect...

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 possible solutions. With local Lipschitz continuity and the so-called AΓ-condition for the comparison principle to hold, we prove the existence of a unique solution under the ge...

The paper develops an asymptotic expansion method for forward-backward SDEs
driven by the random Poisson measures with sigma-finite compensators. The
expansion is performed around the small-variance limit of the forward SDE and
does not necessarily require a small size of the non-linearity in the BSDE's
driver, which was actually the case for the l...

Collateralization with daily margining and the so-called OIS-discounting have
become a new standard in the post-crisis financial market. Although there
appeared a large amount of literature to deal with a so-called multi-curve
framework, a complete picture for a multi-currency setup with currency funding
spreads, which are necessary to explain non-...

This paper deals with an optimal position management problem for a market maker who has to face uncertain customer order flows in an illiquid market, where the market maker’s continuous trading incurs a stochastic linear price impact. Although the execution timing is uncertain, the market maker can also ask its OTC counterparties to transact a bloc...

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 small-diffusion asymptotic
expansion method, the dynamics of variables given by the forward SDEs is
treated exactly. Although it requires a special...

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 small-diffusion asymptotic expansion method, the dynamics of variables given by the forward SDEs is treated exactly. Although it requires a special...

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 information on the relevant processes. In addition to the
market risk, fund and insurance managers have to be prepared for sudden and
possibly contagious changes in the investment...

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 information on the relevant processes. In addition to the market risk, fund and insurance managers have to be prepared for sudden and possibly contagious changes in the investment...

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 of three BSDEs
derived by Mania and Tevzadze (2003) an...

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 of three BSDEs derived by Mania and Tevzadze (2003) an...

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 of an American option price with that of a European
option of the same maturity and the remaining early exercise premium can be
cast into the form of a decoupled non-lin...

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 relevant
conditional distribution. Thanks to the simplici...

We study the pricing of a continuously collateralized credit default swap (CDS). We make use of the “survival measure” to derive the pricing formula in a straightforward way. As a result, we find that, even under a perfect collateralization, there exists an unremovable trace of the counterparty and the investor in the pricing of CDSs due to their d...

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 with non-linear generator and feedback terms, we have shown that it is possible to carry out a recursive approximation to an arbitrarily higher order, where the required ca...

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 will be particularly useful to investigate large
and complex systems, and hence it is a good complement of our previous work
presenting an analytical perturbation procedu...

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 perfectly hedgeable. By combining standard asymptotic
expansion technique for the underlying volatility process, we derive explicit
expression for the solution of the FBSDE u...

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 to the USD silo, where the contracts are collateralized by USD cash, or a different currency with an appropriate interest rate overlay to achieve the same economic effect...

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 with non-linear generator and feedback terms, we have
shown that it is possible to carry out a recursive approximation to an
arbitrarily higher order, where the required ca...

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. As a result, we have found that there exists irremovable trace of the counter party as well as the investor in the price of CDS through their default dependence even unde...

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 with the
associated counter party credit risk. By introducing the...

Collateral has been used for a long time in the cash market and we have also experienced significant increase of its use as an important credit risk mitigation tool in the derivatives market for this decade. Despite its long history in the financial market, its importance for funding has been recognized relatively recently following the explosion o...

In recent years, we have observed dramatic increase of collateralization as an important credit risk mitigation tool in over the counter (OTC) market [6]. Combined with the significant and persistent widening of various basis spreads, such as Libor-OIS and cross currency basis, the practitioners have started to notice the importance of difference b...

Presentation Material for BoJ and FSA.

The recent financial crisis caused dramatic widening and elevated volatilities among basis spreads in cross currency as well as domestic interest rate markets. Furthermore, the widespread use of collateral has made the effective funding cost of financial institutions for the trades significantly different from the Libor of the corresponding payment...

There are now available wide variety of swap products which exchange Libors with different currencies and tenors. Furthermore, the collateralization is becoming more and more popular due to the increased attention to the counter party credit risk. These developments require clear distinction among different type of Libors and the discounting rates....

In recent years, we have observed the dramatic increase of the use of collateral as an important credit risk mitigation tool. It has become even rare to make a contract without collateral agreement among the major financial institutions. In addition to the significant reduction of the counterparty exposure, collateralization has important implicati...

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 the associated CVA. We have presented approximate expr...

The recent financial crisis caused dramatic widening and elevated volatilities among basis spreads in cross currency as well as domestic interest rate markets. Furthermore, the wide spread use of cash collateral, especially in fixed income contracts, has made the effective funding cost of financial institutions for the trades significantly differen...

There are now available wide variety of swap products which exchange Libors with different currencies and tenors. Furthermore, the collateralization is becoming more and more popular due to the increased attention to the counter party credit risk. These developments require clear distinction among different type of Libors and the discounting rates....

The recent financial crisis has spiked the credit and liquidity premia among financial products, and significant widening of basis spreads among Libors with different tenors and currencies has been observed in interest rate markets. Our previous work, "A Note on Construction of Multiple Swap Curves with and without Collateral" has developed an arbi...

The minimal supersymmetric standard model (MSSM) has an unified way of explanation for both the baryon asymmetry and cold dark matter. That is Affleck-Dine baryo/DM-genesis, in which coherent oscillation of squark condensate and its late-time decay produce both of them at the same time. Since both the baryon asymmetry and cold dark matter have the...

The minimal supersymmetric standard model has a truly supersymmetric way of explaining both the baryon asymmetry and cold dark matter in the present Universe: that is, “Affleck-Dine baryo/DM genesis.” The associated late-time decay of Q balls directly connects the origins of the baryon asymmetry and dark matter, and also predicts a specific nature...

Thermal leptogenesis requires the reheating temperature $T_R \gsim 3\times
10^{9}$ GeV, which contradicts a recently obtained constraint on the reheating
temperature, $T_R \lsim 10^6$ GeV, for the gravitino mass of 100 GeV-10 TeV.
This stringent constraint comes from the fact that the hadronic decays of
gravitinos destroy very efficiently light ele...

We show that a mini-thermal inflation occurs naturally in a class of gauge mediation models of supersymmetry (SUSY) breaking, provided that the reheating temperature T_R of the primary inflation is much higher than the SUSY-breaking scale, say T_R > 10^{10} GeV. The reheating process of the thermal inflation produces an amount of entropy, which dil...

We derive a prediction of proton life time based on models of SU(5) unified theories called "semi-simple unification" in this article/talk. Life Time is typically 3 × 1034 - 1035yrs. in the "semi-simple unification models". This article/talk is based on a paper Phys. Lett. B527 106(2002), along with extension of the result obtained there.

In this talk we discuss the origin and nature of the dark matter in the Affleck-Dine (AD) baryogenesis. The AD baryogenesis via most of the flat directions predict formations of large Q-balls, and a great number of the lightest supersymmetric particles (LSPs) are produced nonthermally via the late-time decays of these Q-balls. In order to avoid the...

We point out that there is no cosmological gravitino problem in a certain class of gauge-mediated supersymmetry-breaking (GMSB) models. The constant term in the superpotential naturally causes small mixings between the standard-model and messenger fields, which give rise to late-time decays of the lightest messenger fields. This decay provides an e...

The leptogenesis via the LHU flat direction is the minimal scenario to generate the observed baryon asymmetry in the supersymmetric framework. This scenario is ready to work in the minimal supersymmetric standard model (MSSM) with tiny but nonzero masses of the left-handed neutrinos in the superpotential. The most promising feature of this leptogen...

The formation and late time decays of Q balls are generic consequences of the Affleck-Dine (AD) baryogenesis. A substantial number of the lightest supersymmetry (SUSY) particles (LSPs) are produced nonthermally as the decay products of these Q balls. This requires a significantly large annihilation cross section of the LSP so as not to overclose th...

We show that a class of Affleck--Dine baryogenesis directly relates the
observed mass density of baryons, \Omega_{B}, to that of dark matter,
\Omega_{DM}. In this scenario, the ratio of baryon to dark matter mass density
is solely determined by the low energy parameters, except for an O(0.1)
effective CP-violating phase. We find that \Omega_{B}/\Om...

A no-scale supersymmetry (SUSY) breaking model is investigated in the minimal extension of the minimal supersymmetric standard model (MSSM) with a gauged U(1)B-L symmetry. We specifically consider a unification-inspired model with the gauge groups SU(3)C×SU(2)L×U(1)Y×U(1)B-L⊂SU(5)×U(1)5 for illustration. While the no-scale boundary condition at the...

We discuss two cosmological issues in a generic gauge-mediated supersymmetry (SUSY)-breaking model, namely the Universe's baryon asymmetry and the gravitino dark-matter density. We show that both problems can be simultaneously solved if there exist extra matter multiplets of a SUSY-invariant mass of the order of the ``$\mu$-term'', as suggested in...

If the baryon asymmetry in the present universe is generated by decays of the
$L H_u$ flat direction, the observed baryon asymmetry requires the mass of the
lightest neutrino to be much smaller than the mass scale indicated from the
atmospheric and solar neutrino oscillations. Such a small mass of the lightest
neutrino leads to a high predictabilit...

We investigate the leptogenesis with almost degenerate neutrinos, in the framework of democratic mass matrix, which naturally explains the large mixing angles for neutrino oscillations as well as quark masses and mixing matrix. We find that the baryon asymmetry in the present universe is explained via the decays of right-handed neutrinos produced n...

Semi-simple unification is one of models which naturally solve two difficulties in the supersymmetric grand unification theory: doublet–triplet splitting problem and suppression of dimension 5 proton decay. We analyzed the dimension 6 proton decay of this model using perturbative analysis at the next-to-leading order. The life time of proton is 3×1...

We study the supersymmetric leptogenesis via the LHu flat direction with a gauged U(1)B-L symmetry. We find that the resultant baryon asymmetry is enhanced compared with the case without a gauged U(1)B-L symmetry. The baryon asymmetry is proportional to the reheating temperature of inflation, but it is independent of the gravitino mass. If high reh...

We claim that the higgsino-like and wino-like neutralinos can be good dark matter candidates if they are produced by the late time decay of Q-ball, which is generally formed in Affleck–Dine baryogenesis. The late time decays of the Q-balls into these LSP's and subsequent pair annihilations of the LSP's naturally lead to the desired mass density of...

We briefly review the present status of Affleck-Dine baryogenesis and leptogenesis scenarios in the minimal supersymmetric standard model (MSSM) in the context of the gravity-mediated supersymmetry (SUSY) breaking, and show that there is a serious cosmological problem in the Affleck-Dine mechanism. That is, the late decay of the associated large Q...

In this paper we point out that the cosmological baryon asymmetry in our universe is generated almost independently of the reheating temperature $T_R$ in Affleck-Dine leptogenesis and it is determined mainly by the mass of the lightest neutrino, $m_{\nu_1}$, in a wide range of the reheating temperature $T_R\simeq 10^5$--$10^{12}$ GeV. The present b...

We perform a detailed analysis on Affleck-Dine leptogenesis taking into account the thermal effects on the dynamics of the flat direction field $\phi$. We find that an extremely small mass for the lightest neutrino $\nu_1$, ${m_\nu}_1\lsim 10^{-8}$ eV, is required to produce enough lepton-number asymmetry to explain the baryon asymmetry in the pres...

We claim that the Higgsino-like and wino-like neutralinos can be good darkmatter candidates if they are produced by the late time decay of Q-ball. The latetime decays of the Q-balls into these LSP’s and subsequent pair annihilations ofthe LSP’s naturally lead to the desired mass density of dark matter. Furthermore,these dark matter can be much more...