A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE
Gon\c{c}alo Dos Reis, Ricardo J.N. dos Reis
TL;DR
This paper presents a comparison theorem for quadratic growth FBSDEs, enabling the analysis of control component signs and conditions for their positivity, which advances understanding of these stochastic systems.
Contribution
It introduces a comparison result for quadratic FBSDEs that helps determine the signs and positivity of control processes, a novel theoretical insight.
Findings
Comparison theorem for quadratic FBSDEs established
Conditions for positivity of control processes derived
Componentwise sign analysis of control processes enabled
Abstract
In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.
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