Optimal switching problems with an infinite set of modes: An approach by randomization and constrained backward SDEs
Articolo
Data di Pubblicazione:
2020
Citazione:
Optimal switching problems with an infinite set of modes: An approach by randomization and constrained backward SDEs / M. Fuhrman, M. Morlais. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - 130:5(2020 May), pp. 3120-3153. [10.1016/j.spa.2019.09.008]
Abstract:
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–Jacobi–Bellman equation in our non-Markovian framework.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
stochastic optimal switching; backward SDEs; randomization of controls
Elenco autori:
M. Fuhrman, M. Morlais
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