arXiv subjects

Masaaki Fujii

Publications and source records attributed to Masaaki Fujii.

At least 19 recordsLinked to original sources

arXiv2026

Mean-Field Price Formation on Trees with Multi-Population and Non-Rational Agents

This work solves the equilibrium price formation problem for the risky stock by combining mean-field game theory with the binomial tree framework, adapting the classic approach of Cox, Ross & Rubinstein. For agents with exponential and recursive utilities of exponential-type, we prove the existence of a unique mean-field market-clearing equilibrium and derive an explicit analytic formula for equilibrium transition probabilities of the stock price on the binomial lattice. The agents face stochastic terminal liabilities and incremental endowments that depend on unhedgeable common and idiosyncratic factors, in addition to the stock price path. We also incorporate an external order flow. Furthermore, the analytic tractability of the proposed approach allows us to extend the framework in two important directions: First, we incorporate multi-population heterogeneity, allowing agents to differ in functional forms for their liabilities, endowments, and risk coefficients. Second, we relax the rational expectations hypothesis by modeling agents operating under subjective probability measures which induce stochastically biased views on the stock transition probabilities. Our numerical examples illustrate the qualitative effects of these components on the equilibrium price distribution.

q-fin.MF↗

arXiv2025

Mean-Field Price Formation on Trees with a Network of Relative Performance Concerns

Financial firms and institutional investors are routinely evaluated based on their performance relative to their peers. These relative performance concerns significantly influence risk-taking behavior and market dynamics. While the literature studying Nash equilibrium under such relative performance competitions is extensive, its effect on asset price formation remains largely unexplored. This paper investigates mean-field equilibrium price formation of a single risky stock in a discrete-time market where agents exhibit exponential utility and relative performance concerns. Unlike existing literature that typically treats asset prices as exogenous, we impose a market-clearing condition to determine the price dynamics endogenously within a relative performance equilibrium. Using a binomial tree framework, we establish the existence and uniqueness of the market-clearing mean-field equilibrium in both single- and multi-population settings. Finally, we provide illustrative numerical examples demonstrating the equilibrium price distributions and agents' optimal position sizes.

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arXiv2025

Mean-field equilibrium price formation with exponential utility

In this paper, using the mean-field game theory, we study a problem of equilibrium price formation among many investors with exponential utility in the presence of liabilities unspanned by the security prices. 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 a novel mean-field backward stochastic differential equation (BSDE), whose driver has quadratic growth both in the stochastic integrands and in their conditional expectations. We prove the existence of a solution to the mean-field BSDE under several conditions and show that the resultant risk-premium process actually clears the market in the large population limit.

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arXiv2024

Mean field equilibrium asset pricing model with habit formation

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 equilibrium, we derive a quadratic-growth mean field backward stochastic differential equation (BSDE) and study its well-posedness and asymptotic behavior in the large population limit. Additionally, we introduce an exponential quadratic Gaussian reformulation of the asset pricing model, in which the solution is obtained in a semi-analytic form.

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arXiv2023

Equilibrium pricing of securities in the co-presence of cooperative and non-cooperative populations

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 population limit, the problem for the central planner is shown to be a conditional extended mean-field control. In addition to the convexity assumptions, if the relative size of the cooperative population is small enough, then we are able to show the existence of a unique equilibrium for both the finite-agent and the mean-field models. The strong convergence to the mean-field model is also proved under the same conditions.

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arXiv2022

Open Multi-Access Network Platform with Dynamic Task Offloading and Intelligent Resource Monitoring

We constructed an open multi-access network platform using open-source hardware and software. The open multi-access network platform is characterized by the flexible utilization of network functions, integral management and control of wired and wireless access networks, zero-touch provisioning, intelligent resource monitoring, and dynamic task offloading. We also propose an application-driven dynamic task offloading that utilizes intelligent resource monitoring to ensure effective task processing in edge and cloud servers. For this purpose, we developed a mobile application and server applications for the open multi-access network platform. To investigate the feasibility and availability of our developed platform, we experimentally and analytically evaluated the effectiveness of application-driven dynamic task offloading and intelligent resource monitoring. The experimental results demonstrated that application-driven dynamic task offloading could reduce real-time task response time and traffic over metro and core networks.

cs.NI↗

arXiv2022

Equilibrium Price Formation with a Major Player and its Mean Field Limit

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 their individual clients. The equilibrium price process that balances demand and supply of the securities, including the functional form of the price impact for the major firm, is derived endogenously both in the market of finite population size and in the corresponding mean field limit.

q-fin.MF↗

arXiv2021

Strong Convergence to the Mean-Field Limit of A Finite Agent Equilibrium

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 the current work, under suitable conditions, we show the existence of a finite agent equilibrium and its strong convergence to the corresponding mean-field limit given in [16]. As an important byproduct, we get the direct estimate on the difference of the equilibrium price between the two markets; one consisting of heterogeneous agents of finite population size and the other of homogeneous agents of infinite population size.

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arXiv2021

A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition

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 are interacting through the market price. Adopting a mean field game (MFG) approach, we find a special form of forward-backward stochastic differential equations of McKean-Vlasov type with common noise whose solution provides a good approximate of the market price. We show the convergence of the net order flow to zero in the large N-limit and get the order of convergence in N under some conditions. We also extend the model to a setup with multiple populations where the agents within each population share the same cost and coefficient functions but they can be different population by population.

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arXiv2020

Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations

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 of the state dynamics are shared among the agents within each population, they can be different population by population. We study the mean field limit for the three different situations; (i) every agent is non-cooperative; (ii) the agents within each population are cooperative; and (iii) the agents in some populations are cooperative but those in the other populations are not. We provide several sets of sufficient conditions for the existence of a mean field equilibrium for each of these cases. Furthermore, under appropriate conditions, we show that the mean field solution to each of these problems actually provides an approximate Nash equilibrium for the corresponding game with a large but finite number of agents.

math.PR↗

arXiv2019

Asymptotic Expansion as Prior Knowledge in Deep Learning Method for high dimensional BSDEs

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 using Bergman's model with different lending and borrowing rates as a typical model for FVA as well as a class of solvable BSDEs with quadratic growth drivers. We also present an extension of the deep BSDE solver for reflected BSDEs representing American option prices.

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arXiv2018

Asymptotic Expansion for Forward-Backward SDEs with Jumps

This work provides a semi-analytic approximation method for decoupled forwardbackward 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 provide a semi-analytic solution technique as well as its error estimate for which we only need to solve essentially a system of linear ODEs. In the case of a finite jump measure with a bounded intensity, the method can also handle state-dependent and hence non-Poissonian jumps, which are quite relevant for many practical applications.

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arXiv2018

Anticipated Backward SDEs with Jumps and quadratic-exponential growth drivers

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 quadratic and exponential growth on the spot values of $(Z,ψ)$, respectively. The existence of the unique solution is proved for Markovian and non-Markovian settings with different structural assumptions on the driver. In the former case, some regularities on $(Z,ψ)$ with respect to the forward process are also obtained.

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arXiv2018

Solving Backward Stochastic Differential Equations with quadratic-growth drivers by Connecting the Short-term Expansions

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 numerical integrations for estimating conditional expectations at each space-time node. Numerical examples of quadratic-growth as well as Lipschitz BSDEs suggest that the scheme works well even for large quadratic coefficients, and a fortiori for large Lipschitz constants.

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arXiv2017

Electron--Proton Decoupling in Excited-State Hydrogen Atom Transfer in the Gas Phase

Hydrogen-release by photoexcitation, excited-state- hydrogen-transfer (ESHT), is one of the important photo- chemical processes that occur in aromatic acids and is responsible for photoprotection of biomolecules. The mecha- nism is described by conversion of the initial state to a charge- separated state along the O(N)-H bond elongation, leading to dissociation. Thus ESHT is not a simple H-atom transfer in which a proton and a 1s electron move together. Here we show that the electron-transfer and the proton-motion are decoupled in gas-phase ESHT. We monitor electron and proton transfer independently by picosecond time-resolved near-infrared and infrared spectroscopy for isolated phenol--(ammonia)5, a benchmark molecular cluster. Electron transfer from phenol to ammonia occurred in less than 3 picoseconds, while the overall H-atom transfer took 15 picoseconds. The observed electron-proton decoupling will allow for a deeper understanding and control of of photochemistry in biomolecules

physics.atm-clus↗

arXiv2017

Electron-proton transfer mechanism of excited-state hydrogen transfer in phenol--(NH3)n (n = 3 and 5)

Excited state hydrogen transfer (ESHT) is responsible to various photochemical processes of aromatics including photoprotection of nuclear basis. Its mechanism is explained by the internal conversion from aromatic $π$$π$* to $π$$σ$* states via conical intersection. It means that the electron is transferred to a diffuse Rydberg like $σ$* orbital apart from the proton migration. This picture means the electron and the proton are not move together and its dynamics are different in principle. Here, we have applied the picosecond time-resolved near infrared (NIR) and infrared (IR) spectroscopies to the phenol--(NH 3) 5 cluster, the bench mark system of ESHT, and monitored the electron transfer and proton motion independently. The electron transfer monitored by the NIR transition rises within 3 ps while the overall H transfer detected by the IR absorption of NH vibration appears with the lifetime of $\approx$20 ps. It clearly proves that the electron motion and proton migration are decoupled. Such the difference of the time-evolutions between the NIR absorption and the IR transition has not been detected in the cluster with three ammonia molecules. We will report full of our observation together with theoretical calculations of potential energy surfaces of $π$$π$* and $π$$σ$* states, and will discuss the ESHT mechanism and its cluster size-dependence between n = 3 and 5. It is suggested that the presence and absence of a barrier in the proton transfer coordinate cause the different dynamics. 2

physics.atm-clus↗

arXiv2017

Quadratic-exponential growth BSDEs with Jumps and their Malliavin's Differentiability

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 A_gamma-condition for the comparison principle to hold, we prove the existence of a unique solution under the general quadratic-exponential structure. We have also shown that the strong convergence occurs under more general (not necessarily monotone) sequence of drivers, which is then applied to give the sufficient conditions for the Malliavin's differentiability.

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arXiv2015

A General Framework for the Benchmark pricing in a Fully Collateralized Market

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 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 interest rates in a fully collateralized market. It gives a new formulation of the currency funding spread which is better suited for the general dependence. In the last half, it develops a discretization of the HJM framework with a fixed tenor structure, which makes it implementable as a traditional Market Model.

q-fin.PR↗