67,954 research outputs found
Partial Information Differential Games for Mean-Field SDEs
This paper is concerned with non-zero sum differential games of mean-field
stochastic differential equations with partial information and convex control
domain. First, applying the classical convex variations, we obtain stochastic
maximum principle for Nash equilibrium points. Subsequently, under additional
assumptions, verification theorem for Nash equilibrium points is also derived.
Finally, as an application, a linear quadratic example is discussed. The unique
Nash equilibrium point is represented in a feedback form of not only the
optimal filtering but also expected value of the system state, throughout the
solutions of the Riccati equations.Comment: 7 page
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
Singular mean-field control games with applications to optimal harvesting and investment problems
This paper studies singular mean field control problems and singular mean
field stochastic differential games. Both sufficient and necessary conditions
for the optimal controls and for the Nash equilibrium are obtained. Under some
assumptions the optimality conditions for singular mean-field control are
reduced to a reflected Skorohod problem, whose solution is proved to exist
uniquely. Applications are given to optimal harvesting of stochastic mean-field
systems, optimal irreversible investments under uncertainty and to mean-field
singular investment games. In particular, a simple singular mean-field
investment game is studied where the Nash equilibrium exists but is not unique
Stochastic Control of Memory Mean-Field Processes
By a memory mean-field process we mean the solution of a
stochastic mean-field equation involving not just the current state and
its law at time , but also the state values and
its law at some previous times . Our purpose is to
study stochastic control problems of memory mean-field processes.
- We consider the space of measures on with the
norm introduced by Agram and {\O}ksendal in
\cite{AO1}, and prove the existence and uniqueness of solutions of memory
mean-field stochastic functional differential equations.
- We prove two stochastic maximum principles, one sufficient (a verification
theorem) and one necessary, both under partial information. The corresponding
equations for the adjoint variables are a pair of \emph{(time-) advanced
backward stochastic differential equations}, one of them with values in the
space of bounded linear functionals on path segment spaces.
- As an application of our methods, we solve a memory mean-variance problem
as well as a linear-quadratic problem of a memory process
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