2,694 research outputs found
Optimal switching problems with an infinite set of modes: An approach by randomization and constrained backward SDEs
We address a general optimal switching problem over finite horizon for a stochastic system described
by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for
infinitely many modes (or regimes, i.e. the possible values of the piecewise-constant control process).
We allow all the given coefficients in the model to be path-dependent, that is, their value at any time
depends on the past trajectory of the controlled system. The main aim is to introduce a suitable (scalar)
backward stochastic differential equation (BSDE), with a constraint on the martingale part, that allows
to give a probabilistic representation of the value function of the given problem. This is achieved by
randomization of control, i.e. by introducing an auxiliary optimization problem which has the same value
as the starting optimal switching problem and for which the desired BSDE representation is obtained.
In comparison with the existing literature we do not rely on a system of reflected BSDE nor can we
use the associated Hamilton\u2013Jacobi\u2013Bellman equation in our non-Markovian framework
Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian
We consider Hamilton Jacobi Bellman equations in an inifinite dimensional
Hilbert space, with quadratic (respectively superquadratic) hamiltonian and
with continuous (respectively lipschitz continuous) final conditions. This
allows to study stochastic optimal control problems for suitable controlled
Ornstein Uhlenbeck process with unbounded control processes
Differentiability of backward stochastic differential equations in Hilbert spaces with monotone generators
The aim of the present paper is to study the regularity properties of the
solution of a backward stochastic differential equation with a monotone
generator in infinite dimension. We show some applications to the nonlinear
Kolmogorov equation and to stochastic optimal control
Compactness and asymptotic behavior in nonautonomous linear parabolic equations with unbounded coefficients in
We consider a class of second order linear nonautonomous parabolic equations
in R^d with time periodic unbounded coefficients. We give sufficient conditions
for the evolution operator G(t,s) be compact in C_b(R^d) for t>s, and describe
the asymptotic behavior of G(t,s)f as t-s goes to infinity in terms of a family
of measures mu_s, s in R, solution of the associated Fokker-Planck equation
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