451 research outputs found
A Class of Mean-field LQG Games with Partial Information
The large-population system consists of considerable small agents whose
individual behavior and mass effect are interrelated via their state-average.
The mean-field game provides an efficient way to get the decentralized
strategies of large-population system when studying its dynamic optimizations.
Unlike other large-population literature, this current paper possesses the
following distinctive features. First, our setting includes the partial
information structure of large-population system which is practical from real
application standpoint. Specially, two cases of partial information structure
are considered here: the partial filtration case (see Section 2, 3) where the
available information to agents is the filtration generated by an observable
component of underlying Brownian motion; the noisy observation case (Section 4)
where the individual agent can access an additive white-noise observation on
its own state. Also, it is new in filtering modeling that our sensor function
may depend on the state-average. Second, in both cases, the limiting
state-averages become random and the filtering equations to individual state
should be formalized to get the decentralized strategies. Moreover, it is also
new that the limit average of state filters should be analyzed here. This makes
our analysis very different to the full information arguments of
large-population system. Third, the consistency conditions are equivalent to
the wellposedness of some Riccati equations, and do not involve the fixed-point
analysis as in other mean-field games. The -Nash equilibrium
properties are also presented.Comment: 19 page
A Risk-Sensitive Global Maximum Principle for Controlled Fully Coupled FBSDEs with Applications
This paper is concerned with a kind of risk-sensitive optimal control problem
for fully coupled forward-backward stochastic systems. The control variable
enters the diffusion term of the state equation and the control domain is not
necessarily convex. A new global maximum principle is obtained without assuming
that the value function is smooth. The maximum condition, the first- and
second-order adjoint equations heavily depend on the risk-sensitive parameter.
An optimal control problem with a fully coupled linear forward-backward
stochastic system and an exponential-quadratic cost functional is discussed.
The optimal feedback control and optimal cost are obtained by using Girsanov's
theorem and completion-of-squares approach via risk-sensitive Riccati
equations. A local solvability result of coupled risk-sensitive Riccati
equations is given by Picard-Lindelf's Theorem.Comment: 31 page
LQG Risk-Sensitive Mean Field Games with a Major Agent: A Variational Approach
Risk sensitivity plays an important role in the study of finance and
economics as risk-neutral models cannot capture and justify all economic
behaviors observed in reality. Risk-sensitive mean field game theory was
developed recently for systems where there exists a large number of
indistinguishable, asymptotically negligible and heterogeneous risk-sensitive
players, who are coupled via the empirical distribution of state across
population. In this work, we extend the theory of Linear Quadratic Gaussian
risk-sensitive mean-field games to the setup where there exists one major agent
as well as a large number of minor agents. The major agent has a significant
impact on each minor agent and its impact does not collapse with the increase
in the number of minor agents. Each agent is subject to linear dynamics with an
exponential-of-integral quadratic cost functional. Moreover, all agents
interact via the average state of minor agents (so-called empirical mean field)
and the major agent's state. We develop a variational analysis approach to
derive the best response strategies of agents in the limiting case where the
number of agents goes to infinity. We establish that the set of obtained
best-response strategies yields a Nash equilibrium in the limiting case and an
-Nash equilibrium in the finite player case. We conclude the paper
with an illustrative example
General mean-field BSDEs with diagonally quadratic generators in multi-dimension
The purpose of this paper is to investigate general mean-field backward
stochastic differential equations (MFBSDEs) in multi-dimension with diagonally
quadratic generators , that is, the coefficients depend
not only on the solution processes , but also on their law
, as well as have a diagonally quadratic growth in and
super-linear growth (or even a quadratic growth) in the law of which is
totally new. We start by establishing through a fixed point theorem the
existence and the uniqueness of local solutions in the ``Markovian case''
when the terminal value is
bounded. Afterwards, global solutions are constructed by stitching local
solutions. Finally, employing the -method, we explore the existence and
the uniqueness of global solutions for diagonally quadratic mean-field BSDEs
with convex generators, even in the case of unbounded terminal values that have
exponential moments of all orders. These results are extended to a
Volterra-type case where the coefficients can even be of quadratic growth with
respect to the law of
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