RADNER EQUILIBRIUM AND SYSTEMS OF QUADRATIC BSDES WITH DISCONTINUOUS GENERATORS

被引：1

作者：

Escauriaza, Luis ^{[1
]}

Schwarz, Daniel C. ^{[2
]}

Xing, Hao ^{[3
]}

机构：

[1] Univ Basque Country, Dept Matemat, Bilbao, Spain

[2] UCL, Dept Math, London, England

[3] Boston Univ, Questrom Sch Business, Dept Finance, Boston, MA USA

来源：

ANNALS OF APPLIED PROBABILITY | 2022年 / 32卷 / 05期

关键词：

Backward stochastic differential equations; systems of BSDEs; discontinuous generator; quadratic nonlinearities; general equilibrium; backward uniqueness; unique continuation; STOCHASTIC DIFFERENTIAL-EQUATIONS; UNIQUE CONTINUATION THEOREM; BACKWARD UNIQUENESS; CONTINUOUS-TIME; CARLEMAN INEQUALITIES; PARABOLIC OPERATORS; INCOMPLETE MARKETS; SECURITIES MARKETS; EXISTENCE; LANDIS;

D O I：

10.1214/21-AAP1765

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Motivated by an equilibrium problem, we establish the existence of a solution for a family of Markovian backward stochastic differential equations with quadratic nonlinearity and discontinuity in Z. Using unique continuation and backward uniqueness, we show that the set of discontinuity has measure zero. In a continuous-time stochastic model of an endowment economy, we prove the existence of an incomplete Radner equilibrium with nondegenerate endogenous volatility.

引用

收藏

页码：3492 / 3536

页数：45

相关论文

共 50 条

[21] Quadratic BSDEs with jumps and related PIDEs [J].

Madoui, Imene ;

Eddahbi, Mhamed ;

Khelfallah, Nabil .

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2022, 94 (03) :386-414

[22] Wellposedness of anticipated BSDEs with quadratic growth and unbounded terminal value [J].

Pak, Ji-Gwon ;

Kim, Mun-Chol ;

Kim, Kon-Gun .

BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, 2024, 38 (01) :108-127

[23] Markovian Quadratic BSDEs with an Unbounded Sub-quadratic Growth [J].

Ju, Jingnan ;

Tang, Shanjian .

CHINESE ANNALS OF MATHEMATICS SERIES B, 2024, 45 (03) :441-462

[24] Multidimensional Markovian BSDEs with Jumps and Continuous Generators [J].

Eddahbi, Mhamed ;

Almualim, Anwar ;

Khelfallah, Nabil ;

Madoui, Imene .

AXIOMS, 2023, 12 (01)

[25] Minimal supersolutions of BSDEs with lower semicontinuous generators [J].

Heyne, Gregor ;

Kupper, Michael ;

Mainberger, Christoph .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2014, 50 (02) :524-538

[26] BSDEs with polynomial growth generators in a defaultable market [J].

Guo, Dongmei ;

Leng, Huinan ;

Zhang, Qi .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 404 (02) :459-469

[27] Existence of a Radner equilibrium in a model with transaction costs [J].

Weston, Kim .

MATHEMATICS AND FINANCIAL ECONOMICS, 2018, 12 (04) :517-539

[28] Representation Theorems for Generators of BSDEs in Lp Spaces [J].

Song, Li ;

Hu, Feng ;

Chen, Zeng-jing .

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2012, 28 (02) :255-264

[29] Quadratic BSDEs with jumps: Related nonlinear expectations [J].

Kazi-Tani, Nabil ;

Possamai, Dylan ;

Zhou, Chao .

STOCHASTICS AND DYNAMICS, 2016, 16 (04)

[30] Taylor approximation of incomplete Radner equilibrium models [J].

Jin Hyuk Choi ;

Kasper Larsen .

Finance and Stochastics, 2015, 19 :653-679

← 1 2 3 4 5 →