Existence, Uniqueness and Stability of $$L^1$$ L 1 Solutions for Multidimensional Backward Stochastic Differential Equations with Generators of One-Sided Osgood Type

Fan, Sheng Jun

doi:10.1007/s10959-017-0755-3

Cited by 10 publications

(3 citation statements)

References 34 publications

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“…Such a relationship will lead to many asset pricing anomalies, such as a low risk premium and a γ ψ high risk-free rate. For disentangling risk aversion from EIS, the notion of recursive utilities was first specified in discrete time by Epstein and Zin [17]. Its continuous-time analog was formulated in Duffie and Epstein [15].…”

Section: Introductionmentioning

confidence: 99%

Optimal consumption and portfolio selection with Epstein–Zin utility under general constraints

Feng¹,

Tian

2023

PUQR

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The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. Closed but not necessarily convex constraints are imposed on strategies. The optimal consumption and investment strategies are characterized via a quadratic backward stochastic differential equation (BSDE). Due to the stochastic market environment, solutions to this BSDE are unbounded, so the BMO argument breaks down. After establishing the martingale optimality criterion and carefully selecting Lyapunov functions, the verification theorem is ultimately obtained. In addition, several examples and numerical simulations of optimal strategies are provided and illustrated.

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Section: Introductionmentioning

confidence: 99%

Optimal consumption and portfolio selection with Epstein–Zin utility under general constraints

Feng¹,

Tian

2023

PUQR

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“…As far as we know the only paper concerned with stability results for BSDEs with L 1 -data (we omit in this comment papers with generators independent of z-variable) is the paper by S.J. Fan [2], where the author has proven the following convergence…”

Section: Introductionmentioning

confidence: 99%

“…Fan considered even weaker than (H2) one-sided Osgood condition). In [2] the author conjectured that in general a priori estimates for BSDEs with L 1 -data cannot hold (see the comments in the first paragraph on page 1863 in [2]). Our main result disproves this conjecture.…”

Section: Introductionmentioning

confidence: 99%

A priori estimates for multidimensional BSDEs with integrable data

Klimsiak¹,

Rzymowski²

2022

Preprint

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We study Backward Stochastic Differential Equations on a probability space equipped with a Brownian filtration. We assume that the terminal value and the generator at zero are merely integrable. Moreover, the generator is assumed to be non-increasing with respect to the value variable (with no restrictions on the growth) and Lipschitz continuous, with sublinear growth, with respect to the control variable. We provide a priori estimate and stability result for solutions to the aforementioned BSDEs.

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