Strong solutions of forward–backward stochastic differential equations with measurable coefficients

Luo, Peng; Pamen, Olivier Menoukeu; Tangpi, Ludovic

doi:10.1016/j.spa.2021.10.012

Cited by 3 publications

(2 citation statements)

References 42 publications

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“…Assume that g n (t, x, y, z) = g(t, x, y, z) + n(X(t) − x), so Equation ( 13) can be written as: (14) where A n (t) = t a n(τ − a) ρ−1 (X(τ) − X n (τ))dτ. From Lemma 5 and a comparison theorem, we get that the sequence (X n (t)) n∈N + is increasing and monotonically converges.…”

Section: Doob-meyer Decomposition Theoremmentioning

confidence: 99%

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g-Expectation for Conformable Backward Stochastic Differential Equations

Luo

Fečkan

Wang

et al. 2022

Axioms

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In this paper, we study the applications of conformable backward stochastic differential equations driven by Brownian motion and compensated random measure in nonlinear expectation. From the comparison theorem, we introduce the concept of g-expectation and give related properties of g-expectation. In addition, we find that the properties of conformable backward stochastic differential equations can be deduced from the properties of the generator g. Finally, we extend the nonlinear Doob–Meyer decomposition theorem to more general cases.

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Section: Doob-meyer Decomposition Theoremmentioning

confidence: 99%

“…In addition, coupled forward backward stochastic differential equations driven by the G-Brownian motion were studied in [13], while [14] investigated the solvability of fully coupled forward-backward stochastic differential equations with irregular coefficients.…”

Section: Introductionmentioning

confidence: 99%

g-Expectation for Conformable Backward Stochastic Differential Equations

Luo

Fečkan

Wang

et al. 2022

Axioms

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Maximum Principle for Stochastic Control of SDEs with Measurable Drifts

Pamen

Tangpi

2023

J Optim Theory Appl

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In this paper, we consider stochastic optimal control of systems driven by stochastic differential equations with irregular drift coefficient. We establish a necessary and sufficient stochastic maximum principle. To achieve this, we first derive an explicit representation of the first variation process (in the Sobolev sense) of the controlled diffusion. Since the drift coefficient is not smooth, the representation is given in terms of the local time of the state process. Then we construct a sequence of optimal control problems with smooth coefficients by an approximation argument. Finally, we use Ekeland’s variational principle to obtain an approximating adjoint process from which we derive the maximum principle by passing to the limit. The work is notably motivated by the optimal consumption problem of investors paying wealth tax.

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