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13 results on '"Yiqing Lin"'

1. Utility Maximization Problem with Transaction Costs: Optimal Dual Processes and Stability

Author

Yiqing Lin, Lingqi Gu, and Junjian Yang

Subjects
0209 industrial biotechnology, Numéraire, Mathematical optimization, Control and Optimization, Applied Mathematics, Shadow price, 010102 general mathematics, Stability (learning theory), 02 engineering and technology, 01 natural sciences, Dual (category theory), Complement (complexity), 020901 industrial engineering & automation, Semimartingale, Utility maximization problem, Convergence (routing), 0101 mathematics, Mathematics
Abstract

In this paper, we investigate the stability problem of the numeraire-based utility maximization problem in markets with transaction costs, where the stock price is not necessarily a semimartingale. Precisely, the static stability of primal and dual value functions as well as the convergence of primal and dual optimizers are presented when perturbations occur in the utility function and in the physical probability. Furthermore, this study focuses on the optimal dual process (ODP), which induces the dual optimizer and attains optimality for a dynamical dual problem. Properties of ODPs are discussed which are complement of the duality theory for this utility maximization problem. When the parameters of the market and the investor are slightly perturbed, both the dual optimizer and the associated optimal dual process are stable. Thus, a shadow price process is constructed based on the sequence of ODPs corresponding to problems with small misspecified parameters.

Published
2020
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2. On properties of solutions to Black–Scholes–Barenblatt equations

Author

Weicheng Xu, Yiqing Lin, and Xinpeng Li

Subjects
Comparison theorem, Strict comparison theorem, Algebra and Number Theory, Partial differential equation, Functional analysis, Applied Mathematics, lcsh:Mathematics, 010102 general mathematics, Sigma, Strict sub-additivity, lcsh:QA1-939, 01 natural sciences, 010101 applied mathematics, Ordinary differential equation, Black–Scholes–Barenblatt equation, 0101 mathematics, Analysis, Mathematical physics, Mathematics
Abstract

This paper is concerned with the Black–Scholes–Barenblatt equation $\partial _{t}u+r(x\partial _{x}u-u)+G(x^{2}\partial _{xx}u)=0$ , where $G(\alpha )=\frac{1}{2}(\overline{\sigma}^{2}-\underline{\sigma}^{2})|\alpha |+\frac{1}{2}(\overline{\sigma}^{2}+\underline{\sigma}^{2})\alpha $ , $\alpha \in \mathbb{R}$ . This equation is usually used for derivative pricing in the financial market with volatility uncertainty. We discuss a strict comparison theorem for Black–Scholes–Barenblatt equations, and study strict sub-additivity of their solutions with respect to terminal conditions.

Published
2019
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3. Quadratic backward stochastic differential equations driven by G-Brownian motion: Discrete solutions and approximation

Author

Ying Hu, Yiqing Lin, and Abdoulaye Soumana Hima

Subjects
Statistics and Probability, Quadratic growth, Girsanov theorem, Discretization, Applied Mathematics, 010102 general mathematics, Banach space, 01 natural sciences, 010104 statistics & probability, Stochastic differential equation, Nonlinear system, Modeling and Simulation, Applied mathematics, Uniqueness, 0101 mathematics, Brownian motion, Mathematics
Abstract

In this paper, we consider backward stochastic differential equations driven by G -Brownian motion (GBSDEs) under quadratic assumptions on coefficients. We prove the existence and uniqueness of solution for such equations. On the one hand, a priori estimates are obtained by applying the Girsanov type theorem in the G -framework, from which we deduce the uniqueness. On the other hand, to prove the existence of solutions, we first construct solutions for discrete GBSDEs by solving corresponding fully nonlinear PDEs, and then approximate solutions for general quadratic GBSDEs in Banach spaces.

Published
2018
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4. Quadratic BSDEs with mean reflection

Author

Peng Luo, Yiqing Lin, Hélène Hibon, Falei Wang, Ying Hu, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [ETH Zurich] (D-MATH), Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich), Shandong Jiaotong University [Jinan], Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Centre de Mathématiques Appliquées - Ecole Polytechnique ( CMAP ), École polytechnique ( X ) -Centre National de la Recherche Scientifique ( CNRS ), Departement of Mathematics, ETH Zurich, Eidgenössische Technische Hochschule [Zürich] ( ETH Zürich ), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), and ANR-16-CE40-0015,MFG,Jeux Champs Moyen(2016)

Subjects
Control and Optimization, Interval (mathematics), BMO martingales, 01 natural sciences, 60H10, 60H30, 010104 statistics & probability, Quadratic equation, Mathematics::Probability, FOS: Mathematics, Uniform boundedness, Contraction mapping, BSDEs with mean reflection, 0101 mathematics, Mathematics, Quadratic growth, Discrete mathematics, Generator (category theory), Applied Mathematics, Probability (math.PR), 010102 general mathematics, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Reflection (mathematics), quadratic generators, Bounded function, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Mathematics - Probability
Abstract

International audience; The present paper is devoted to the study of the well-posedness of BSDEs with mean reflection whenever the generator has quadratic growth in the $z$ argument. This work is the sequel of Briand et al. [BSDEs with mean reflection, arXiv:1605.06301] in which a notion of BSDEs with mean reflection is developed to tackle the super-hedging problem under running risk management constraints. By the contraction mapping argument, we first prove that the quadratic BSDE with mean reflection admits a unique deterministic flat local solution on a small time interval whenever the terminal value is bounded. Moreover, we build the global solution on the whole time interval by stitching local solutions when the generator is uniformly bounded with respect to the $y$ argument.

Published
2018
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5. Strict comparison theorems under sublinear expectations

Author

Yiqing Lin and Xinpeng Li

Subjects
Discrete mathematics, Comparison theorem, Partial differential equation, Sublinear function, Lipschitz class, General Mathematics, 010102 general mathematics, Space (mathematics), 01 natural sciences, Omega, 010104 statistics & probability, Nonlinear system, 0101 mathematics, Mathematics
Abstract

In this paper, we consider strict comparison theorems in the framework of G-expectation, which is a type of sublinear expectation associated with fully nonlinear parabolic partial differential equations. In particular, we first apply Krylov–Safonov estimates to establish the strict comparison theorem for functions from the Lipschitz class $$Lip(\Omega )$$ . Then we prove generalized strict comparison theorems on the enlarged space $$L_G^1(\Omega )$$ , which is the Banach completion of $$Lip(\Omega )$$ under the G-expectation.

Published
2017
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6. Second order backward SDE with random terminal time

Author

Nizar Touzi, Junjian Yang, Yiqing Lin, Zhenjie Ren, Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Fakultät für Mathematik und Geoinformation [Wien] (TU Wien), and Vienna University of Technology (TU Wien)

Subjects
Statistics and Probability, Mathematics::Analysis of PDEs, Backward SDE, Context (language use), 01 natural sciences, 60H10, 60H30, 010104 statistics & probability, Stochastic differential equation, Mathematics::Probability, Stopping time, FOS: Mathematics, second order backward SDE, Applied mathematics, [MATH]Mathematics [math], 0101 mathematics, Mathematics - Optimization and Control, Martingale representation theorem, Mathematics, quasi-sure stochastic analysis, Markov chain, Probability (math.PR), 010102 general mathematics, 16. Peace & justice, Nonlinear system, Optimization and Control (math.OC), random horizon, Heat equation, 60H10, Statistics, Probability and Uncertainty, 60H30, Random variable, Mathematics - Probability
Abstract

Backward stochastic differential equations extend the martingale representation theorem to the nonlinear setting. This can be seen as path-dependent counterpart of the extension from the heat equation to fully nonlinear parabolic equations in the Markov setting. This paper extends such a nonlinear representation to the context where the random variable of interest is measurable with respect to the information at a finite stopping time. We provide a complete wellposedness theory which covers the semilinear case (backward SDE), the semilinear case with obstacle (reflected backward SDE), and the fully nonlinear case (second order backward SDE).

Published
2020
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7. Causal Transport in Discrete Time and Applications

Author

Julio Backhoff, Mathias Beiglböck, Anastasiia Zalashko, and Yiqing Lin

Subjects
Stochastic process, Probability (math.PR), 010102 general mathematics, 90C15, 60G70, 39B62, Gauge (firearms), 01 natural sciences, Theoretical Computer Science, Dynamic programming, Causality (physics), 010104 statistics & probability, Noise, Discrete time and continuous time, Optimization and Control (math.OC), FOS: Mathematics, Applied mathematics, Relaxation (approximation), 0101 mathematics, Mathematics - Optimization and Control, Mathematics - Probability, Software, Mathematics
Abstract

Loosely speaking, causal transport plans are a relaxation of adapted processes in the same sense as Kantorovich transport plans extend Monge-type transport maps. The corresponding causal version of the transport problem has recently been introduced by Lassalle. Working in a discrete time setup, we establish a dynamic programming principle that links the causal transport problem to the transport problem for general costs recently considered by Gozlan et al. Based on this recursive principle, we give conditions under which the celebrated Knothe-Rosenblatt rearrangement can be viewed as a causal analogue to the Brenier's map. Moreover, these considerations provide transport-information inequalities for the nested distance between stochastic processes pioneered by Pflug and Pichler, and so serve to gauge the discrepancy between stochastic programs driven by different noise distributions., We added a characterization of the Knothe-Rosenblatt rearrangement in terms of increasing triangular transformations, 25 pages

Published
2017
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8. Reflected stochastic differential equations driven by $G$-Brownian motion in non-convex domains

Author

Abdoulaye Soumana Hima, Yiqing Lin, Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Département de Mathématiques - Université de Maradi, Université Dan Dicko Dan koulodo de Maradi (UDDM), Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), 321111, European Research Council, ANR-11-LABX-0020-01, ANR, ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), Centre de Mathématiques Appliquées - Ecole Polytechnique ( CMAP ), École polytechnique ( X ) -Centre National de la Recherche Scientifique ( CNRS ), Université de Maradi, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)

Subjects
Banach space, Hölder condition, 01 natural sciences, Skorokhod integral, 010104 statistics & probability, Stochastic differential equation, Mathematics::Probability, FOS: Mathematics, Uniqueness, 0101 mathematics, Brownian motion, Mathematics, Geometric Brownian motion, Skorokhod problem, Hölder continuity, Probability (math.PR), 010102 general mathematics, Mathematical analysis, stochastic differential equations, non-convex reflecting boundaries, Stochastic partial differential equation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], G-Brownian motion, Modeling and Simulation, 60H10, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Mathematics - Probability
Abstract

In this paper, we first review the penalization method for solving deterministic Skorokhod problems in non-convex domains and establish estimates for problems with [Formula: see text]-Hölder continuous functions. With the help of these results obtained previously for deterministic problems, we pathwisely define the reflected [Formula: see text]-Brownian motion and prove its existence and uniqueness in a Banach space. Finally, multi-dimensional reflected stochastic differential equations driven by [Formula: see text]-Brownian motion are investigated via a fixed-point argument.

Published
2019
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9. Generalized Wasserstein Distance and Weak Convergence of Sublinear Expectations

Author

Yiqing Lin and Xinpeng Li

Subjects
Statistics and Probability, 050208 finance, Sublinear function, Weak convergence, General Mathematics, Probability (math.PR), 010102 general mathematics, 05 social sciences, Mathematical analysis, 01 natural sciences, 0502 economics and business, FOS: Mathematics, Applied mathematics, 0101 mathematics, Statistics, Probability and Uncertainty, Mathematics - Probability, Computer Science::Databases, Mathematics, Probability measure
Abstract

In this paper, we define the generalized Wasserstein distance for sets of Borel probability measures and demonstrate that the weak convergence of sublinear expectations can be characterized by means of this distance.

Published
2015
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10. Utility maximization problem with random endowment and transaction costs: when wealth may become negative

Author

Junjian Yang and Yiqing Lin

Subjects
Statistics and Probability, Transaction cost, 050208 finance, 91B16, 91G10, Endowment, Applied Mathematics, Shadow price, 05 social sciences, Utility maximization, Probability (math.PR), 01 natural sciences, Mathematical Finance (q-fin.MF), Microeconomics, FOS: Economics and business, 010104 statistics & probability, Utility maximization problem, Quantitative Finance - Mathematical Finance, 0502 economics and business, 8. Economic growth, FOS: Mathematics, 0101 mathematics, Statistics, Probability and Uncertainty, Expected utility hypothesis, Mathematics - Probability, Mathematics
Abstract

In this paper we study the problem of maximizing expected utility from the terminal wealth with proportional transaction costs and random endowment. In the context of the existence of consistent price systems, we consider the duality between the primal utility maximization problem and the dual one, which is set up on the domain of finitely additive measures. In particular, we prove duality results for utility functions supporting possibly negative values. Moreover, we construct the shadow market by the dual optimal process and consider the utility based pricing for random endowment.

Published
2016
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11. A New existence result for Second Order BSDEs with Quadratic Growth and its Applications

Author

Yiqing Lin, Fakultät für Mathematik, Universität Wien, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Fakultät für Mathematik [Wien], Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), FA506041, European Research Council, Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)

Subjects
Statistics and Probability, Quadratic growth, Class (set theory), 010102 general mathematics, Utility maximization, MathematicsofComputing_NUMERICALANALYSIS, robust utility maximization, 01 natural sciences, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 60H10, 60H30, 010104 statistics & probability, Nonlinear system, Stochastic differential equation, second order BSDEs, Modeling and Simulation, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, quadratic growth, Order (group theory), Applied mathematics, 0101 mathematics, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Mathematics
Abstract

In this paper, we study a class of second-order backward stochastic differential equations with quadratic growth in coefficients. In particular, we provide an existence result for these equations and give their applications by solving robust utility maximization problems and introducing a type of nonlinear evaluations.

Published
2016
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12. On the dual problem of utility maximization in incomplete markets

Author

Lingqi Gu, Yiqing Lin, and Junjian Yang

Subjects
Statistics and Probability, Applied Mathematics, 010102 general mathematics, Utility maximization, Probability (math.PR), 90B28, 91B16, 01 natural sciences, Dual (category theory), Terminal value, 010104 statistics & probability, Mathematics::Probability, Optimization and Control (math.OC), Modeling and Simulation, Bounded function, Incomplete markets, Local martingale, FOS: Mathematics, 0101 mathematics, Expected utility maximization, Mathematical economics, Mathematics - Optimization and Control, Brownian motion, Mathematics - Probability, Mathematics
Abstract

In this paper, we study the dual problem of the expected utility maximization in incomplete markets with bounded random endowment. We start with the problem formulated in Cvitanic et al. (2001) and prove the following statement: in the Brownian framework, the countably additive part Q r of the dual optimizer Q ∈ ( L ∞ ) ∗ obtained in Cvitanic et al. (2001) can be represented by the terminal value of a supermartingale deflator Y defined in Kramkov and Schachermayer (1999), which is a local martingale.

Published
2015
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13. Stochastic Differential Equations Driven by $G$-Brownian Motion with Reflecting Boundary Conditions

Author

Yiqing Lin, Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), and Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS )

Subjects
Statistics and Probability, Stochastic calculus, Increasing Processes, $G$-expectation, G-expectation, 01 natural sciences, $G$-It\^o's formula, 010104 statistics & probability, Stochastic differential equation, FOS: Mathematics, Boundary value problem, $G$-stochastic differential equations, 0101 mathematics, G-Itô's formula, Reflecting Boundary Conditions, Brownian motion, Mathematics, Geometric Brownian motion, Probability (math.PR), 010102 general mathematics, Mathematical analysis, Stochastic partial differential equation, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], G-Brownian motion, Local time, G-stochastic differential equations, $G$-Brownian motion, Increasing process, 60H10, Statistics, Probability and Uncertainty, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Mathematics - Probability
Abstract

International audience; In this paper, we introduce the idea of integral with respect to increasing processes under the framework of $G$-expectation and give the proof of extended $G$-Itô's formula. Moreover, we study the existence and uniqueness of solutions to the scalar valued stochastic differential equations driven by $G$-Brownian motion with reflecting boundary conditions (RGSDEs), and give a comparison theorem.

Published
2013
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