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In this article, we consider the solvability problems for the fully coupled forward-backward stochastic difference equations (FBSΔEs). On one hand, we provide the necessary and sufficient condition for the solvability of the linear FBSΔEs. On the other hand, under the assumption that the coefficients satisfy the monotonicity condition, we investigate the existence and uniqueness theorems for the general non linear FBSΔEs. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the existence and uniqueness theorem for backward stochastic differential equation driven by G-Brownian motion (G-BSDE) under degenerate case. Moreover, we propose a new probabilistic method based on the representation theorem of G-expectation and weak convergence to obtain the regularity of fully nonlinear PDE associated to G-BSDE. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general modeling framework for optimal control of stochastic fully coupled forward-backward linear quadratic (FBLQ) problems with indefinite control weight costs that stem from rational expectations models. We propose a new decoupling technique to obtain the optimal feedback control, which is accompanied by one kind of non-Riccati-type ordinary differential equation (ODE). By applying the completion-of-squares method, we prove the existence of the solutions for the obtained ODEs. The obtained results make it possible to compute the control and value function. For this FBLQ problem, the optimal control should depend on the entire trajectory of the state process. Several examples are given to illustrate our results. Funding: M. Hu's research was supported by the National Science Foundation (NSF) [Grant 11671231] and the Young Scholars Program of Shandong University [Grant 2016WLJH10]. S. Ji's research was supported by the NSF [Grant 11571203]. X. Xue's research was supported by "The Fundamental Research Funds of Shandong University," the NSF [Grants 12001316 and 61907022], and the Natural Science Foundation of Shandong Province [Grant ZR2019BF015]. [ABSTRACT FROM AUTHOR]

In this paper, we consider the solvability problems for the fully coupled forward–backward stochastic difference equations (FBSΔEs) on spaces related to discrete time, finite state processes. On one hand, we provide the necessary and sufficient condition for the solvability of the linear FBSΔEs. On the other hand, under the assumption that the coefficients satisfy the monotonicity condition, we investigate the existence and uniqueness theorems for the general nonlinear FBSΔEs. [ABSTRACT FROM AUTHOR]

In this paper, we study the maximum principle for stochastic optimal control problems of forward–backward stochastic difference systems (FBSΔSs). Two types of FBSΔSs are investigated. The first one is described by a partially coupled forward–backward stochastic difference equation (FBSΔE) and the second one is described by a fully coupled FBSΔE. By adopting an appropriate representation of the product rule and an appropriate formulation of the adjoint process, we deduce the adjoint difference equation. Finally, the maximum principle for this optimal control problem with the control domain being convex is established. [ABSTRACT FROM AUTHOR]

This article studies the maximum principle for stochastic optimal control problems of forward‐backward stochastic difference systems (FBSΔSs) where the uncertainty is modeled by a discrete time, finite state process, rather than white noises. Two distinct forms of FBSΔSs are investigated. The first one is described by a partially coupled forward‐backward stochastic difference equation (FBSΔE) and the second one is described by a fully coupled FBSΔE. We deduce the adjoint difference equation by adopting an appropriate representation of the product rule and a proper formulation of the backward stochastic difference equation (BSΔE). Finally, the maximum principle for this optimal control problem with the convex control domain is established. [ABSTRACT FROM AUTHOR]

In many situations, decisions under uncertainty are made with incomplete confidence about the probability law describing the environment (model uncertainty, or ambiguity), but with the opportunity to learn, at some cost, before choosing between actions. In "Optimal Learning Under Robustness and Time-Consistency," Epstein and Ji use a stylized model to derive the optimal demand for learning (or sampling) and how it is affected by model uncertainty. A presumption is that the decision maker is conservative and seeks to make robust decisions. One surprising result is that, in a sequential hypothesis-testing context, sensitivity analysis overstates the robustness value of sampling. In a different context where there exists an unambiguous (purely risky) action, but where learning is not feasible, Ellsberg has highlighted the intuition for choosing the risky option over ambiguous ones. In contrast, Epstein and Ji demonstrate that where learning is feasible and optimal, then the risky action cannot be optimal. We model learning in a continuous-time Brownian setting where there is prior ambiguity. The associated model of preference values robustness and is time-consistent. It is applied to study optimal learning when the choice between actions can be postponed, at a per-unit-time cost, in order to observe a signal that provides information about an unknown parameter. The corresponding optimal stopping problem is solved in closed form, with a focus on two specific settings: Ellsberg's two-urn thought experiment expanded to allow learning before the choice of bets, and a robust version of the classical problem of sequential testing of two simple hypotheses about the unknown drift of a Wiener process. In both cases, the link between robustness and the demand for learning is studied. [ABSTRACT FROM AUTHOR]

In this paper, we study a stochastic recursive optimal control problem in which the value functional is defined by the solution of a backward stochastic differential equation (BSDE) under G-expectation. Under standard assumptions, we establish the comparison theorem for this kind of BSDE and give a novel and simple method to obtain the dynamic programming principle. Finally, we prove that the value function is the unique viscosity solution to a type of fully nonlinear HJB equation. [ABSTRACT FROM AUTHOR]

This paper explores the relationship between non-Markovian fully coupled forward–backward stochastic systems and path-dependent PDEs. The definition of classical solution for the path-dependent PDE is given within the framework of functional Itô calculus. Under mild hypotheses, we prove that the forward–backward stochastic system provides the unique classical solution to the path-dependent PDE. [ABSTRACT FROM AUTHOR]

In this paper, we study the minimum mean square estimator for non-bounded random variables under sublinear operators. The existence and uniqueness of the minimum mean square estimator are obtained. Several properties of the minimum mean square estimator for non-bounded random variables are proved under some mild assumptions. [ABSTRACT FROM AUTHOR]

Recently, the deep learning method has been used for solving forward–backward stochastic differential equations (FBSDEs) and parabolic partial differential equations, as it has good accuracy and performance for high-dimensional problems. In this article, we mainly solve fully coupled FBSDEs through deep learning and provide three algorithms, and the numerical results show remarkable performance, especially for high-dimensional cases. [ABSTRACT FROM AUTHOR]

Within the framework of viscosity solution, we study the relationship between the maximum principle (MP) from M. Hu, S. Ji and X. Xue [SIAM J. Control Optim.56 (2018) 4309–4335] and the dynamic programming principle (DPP) from M. Hu, S. Ji and X. Xue [SIAM J. Control Optim.57 (2019) 3911–3938] for a fully coupled forward–backward stochastic controlled system (FBSCS) with a nonconvex control domain. For a fully coupled FBSCS, both the corresponding MP and the corresponding Hamilton–Jacobi–Bellman (HJB) equation combine an algebra equation respectively. With the help of a new decoupling technique, we obtain the desirable estimates for the fully coupled forward–backward variational equations and establish the relationship. Furthermore, for the smooth case, we discover the connection between the derivatives of the solution to the algebra equation and some terms in the first-order and second-order adjoint equations. Finally, we study the local case under the monotonicity conditions as from J. Li and Q. Wei [SIAM J. Control Optim.52 (2014) 1622–1662] and Z. Wu [Syst. Sci. Math. Sci.11 (1998) 249–259], and obtain the relationship between the MP from Z. Wu [Syst. Sci. Math. Sci.11 (1998) 249–259] and the DPP from J. Li and Q. Wei [SIAM J. Control Optim.52 (2014) 1622–1662]. [ABSTRACT FROM AUTHOR]

This paper considers the stochastic linear quadratic optimal control problem in which the control domain is nonconvex. By the functional analysis and convex perturbation methods, we establish a novel maximum principle. The application of the proposed maximum principle is illustrated through a work-out example. [ABSTRACT FROM AUTHOR]

This paper concerns the recursive utility maximization problem. We assume that the coefficients of the wealth equation and the recursive utility are concave. Then some interesting and important cases with nonlinear and nonsmooth coefficients satisfy our assumption. After given an equivalent backward formulation of our problem, we employ the Fenchel-Legendre transform and derive the corresponding variational formulation. By the convex duality method, the primal "sup-inf" problem is translated to a dual minimization problem and the saddle point of our problem is derived. Finally, we obtain the optimal terminal wealth. To illustrate our results, three cases for investors with ambiguity aversion are explicitly worked out under some special assumptions. [ABSTRACT FROM AUTHOR]

This paper concerns the recursive utility maximization problem for terminal wealth under partial information. We first transform our problem under partial information into the one under full information. When the generator of the recursive utility is concave, we adopt the variational formulation of the recursive utility which leads to a stochastic game problem and characterization of the saddle point of the game is obtained. Then, we study the K-ignorance case and explicit saddle points of several examples are obtained. At last, when the generator of the recursive utility is smooth, we employ the terminal perturbation method to characterize the optimal terminal wealth. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic optimal control problem is investigated in which the system is governed by a stochastic functional differential equation. In the framework of functional Itô calculus, we build the dynamic programming principle and the related path-dependent Hamilton-Jacobi-Bellman equation. We prove that the value function is the viscosity solution of the path-dependent Hamilton-Jacobi-Bellman equation. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: The Neyman–Pearson fundamental lemma is generalized under g-probability. With convexity assumptions, a sufficient and necessary condition which characterizes the optimal randomized tests is obtained via a maximum principle for stochastic control. To cite this article: S. Ji, X.Y. Zhou, C. R. Acad. Sci. Paris, Ser. I 346 (2008). [Copyright &y& Elsevier]

Background: Long noncoding RNA (lncRNA) exerts a potential regulatory role in tumorigenesis. LncRNA NEAT1 expression remains high in osteosarcoma tissues. However, its biological mechanism in osteosarcoma remains unknown. Methods: In this study, NEAT1 expression in osteosarcoma cells was detected by qRT‐PCR. Proliferative and apoptosis potentials of osteosarcoma cells were determined by CCK‐8 assay and Flow Cytometry, respectively. We identified the potential target of NEAT1 through bioinformatics and dual‐luciferase reporter gene assay. Furthermore, their interaction and functions in regulating the development of osteosarcoma were clarified by Western blot and RIP assay. Results: Our results demonstrated a high expression of NEAT1 in osteosarcoma tissues and cells. Overexpression of NEAT1 markedly accelerated proliferative and reduced apoptosis potentials of osteosarcoma cells. Besides, NEAT1 could positively regulate the expression of HOXA13 by competing with miR‐34a‐5p. Conclusion: These results indicated that NEAT1 participated in the development of osteosarcoma as a ceRNA to competitively bind to miR‐34a‐5p and thus mediate HOXA13 expression. [ABSTRACT FROM AUTHOR]

BACKGROUND Osteosarcoma (OS) is the most prevalent malignant primary bone tumor, resulting from severe transformation of primitive mesenchymal cells, which induces osteogenesis. Long non-coding RNA (lncRNA) MSC-AS1 triggers osteogenic differentiation by sponging microRNA (miR)-140-5p. The present study assessed the mechanism of lncRNA MSC-AS1 in OS biological features and sensitivity to cisplatin (DDP) by binding to miR-142. MATERIAL AND METHODS Firstly, lncRNA MSC-AS1 expression in OS tissues and cells was analyzed. OS cells were transfected with silenced MSC-AS1 to determine its role in OS biological behaviors, and we also assessed the effect of MSC-AS1 on OS sensitivity to DDP. Then, website prediction and dual-luciferase reporter gene assay were utilized for verification of the binding site between MSC-AS1 and miR-142. Reverse transcription-quantitative polymerase chain reaction (RT-qPCR) and Western blot analysis were performed to determine the effect of MSC-AS1 on expression of miR-142, cyclin-dependent kinase 6 (CDK6), and the PI3K/AKT signaling pathway. Xenograft transplantation was also applied to confirm the in vitro experiments. RESULTS Overexpressed MSC-AS1 was associated with poor prognosis of OS patients. OS cell proliferation, invasion, and migration were reduced after silencing MSC-AS1, while cell apoptosis was enhanced. Moreover, silencing MSC-AS1 made OS cells more sensitive to DDP. Interestingly, MSC-AS1 knockdown induced miR-142 expression and reduced CDK6 levels, thereby decreasing the protein expression of p-PI3K/t-PI3K and p-AKT/t-AKT. Silencing MSC-AS1 repressed OS progression in vivo. CONCLUSIONS Our study demonstrated that silencing MSC-AS1 inhibited OS biological behaviors by enhancing miR-142 to decrease CDK6 and inactivating the PI3K/AKT axis. Our results may provide new insights for OS treatment.