On relaxed stochastic optimal control for stochastic differential equations driven by G-Brownian motion

Redjil, Amel; Choutri, Salah Eddine

doi:10.48550/arxiv.1702.08735

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2022

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“…This framework was originally introduced by Peng [14], and developed by the stochastic control community later on, see e.g. [15,18]. In this setting, the standard Brownian motion is replaced by a so-called G-Brownian motion, that is modelled as a stochastic process whose distribution is the product of a standard Gaussian with a Lipschitz map, and whose role is to transform the coherent risk measure into a standard, though non-linear expectation.…”

Section: Introductionmentioning

confidence: 99%

First-Order Pontryagin Maximum Principle for Risk-Averse Stochastic Optimal Control Problems

Bonalli¹,

Bonnet²

2022

Preprint

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In this paper, we derive a set of first-order Pontryagin optimality conditions for a risk-averse stochastic optimal control problem subject to final time inequality constraints, and whose cost is a general finite coherent risk measure. Unlike previous contributions in the literature, our analysis holds for classical stochastic differential equations driven by standard Brownian motions. Moreover, it presents the advantages of neither involving second-order adjoint equations, nor leading to the so-called weak version of the PMP, in which the maximization condition with respect to the control variable is replaced by the stationarity of the Hamiltonian.

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Section: Introductionmentioning

confidence: 99%