Monotone stability of quadratic semimartingales with applications to unbounded general quadratic BSDEs

DOI10.1214/12-AOP743zbMath1312.60052arXiv1101.5282OpenAlexW2591655259MaRDI QIDQ373548

Pauline Barrieu, Nicole El Karoui

Publication date: 17 October 2013

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.5282

zbMATH Keywords

strong convergenceinf-convolutionquadratic backward stochastic differential equationsentropic inequalitiesBMO-martingalesexponential transformationmonotone stabilityquadratic semimartingales

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Utility theory (91B16) Generalizations of martingales (60G48) Martingales with continuous parameter (60G44) General theory of stochastic processes (60G07) Auctions, bargaining, bidding and selling, and other market models (91B26) Stochastic analysis (60H99)

Related Items (54)

A characterization of solutions of quadratic BSDEs and a new approach to existence ⋮ Quadratic backward stochastic differential equations driven by \(G\)-Brownian motion: discrete solutions and approximation ⋮ On the Monotone Stability Approach to BSDEs with Jumps: Extensions, Concrete Criteria and Examples ⋮ Incomplete Stochastic Equilibria with Exponential Utilities Close to Pareto Optimality ⋮ Solvability of some quadratic BSDEs without exponential moments ⋮ Some results on general quadratic reflected BSDEs driven by a continuous martingale ⋮ A Global Stochastic Maximum Principle for Forward-Backward Stochastic Control Systems with Quadratic Generators ⋮ Quadratic reflected BSDEs and related obstacle problems for PDEs ⋮ Consistent utility of investment and consumption: a forward/backward SPDE viewpoint ⋮ Quadratic BSDEs with jumps and related PIDEs ⋮ Local existence and uniqueness of solutions to quadratic BSDEs with weak monotonicity and general growth generators ⋮ One dimensional BSDEs with logarithmic growth application to PDEs ⋮ On the uniqueness result for the BSDE with deterministic coefficient ⋮ Existence result for the BSDE with superquadratic growth ⋮ Multi-dimensional backward stochastic differential equations of diagonally quadratic generators: the general result ⋮ Quadratic expansions in optimal investment with respect to perturbations of the semimartingale model ⋮ Existence of global solutions for multi-dimensional coupled FBSDEs with diagonally quadratic generators ⋮ Existence, uniqueness and comparison theorem on unbounded solutions of scalar super-linear BSDEs ⋮ Solvability of coupled FBSDEs with diagonally quadratic generators ⋮ BSDEs with diffusion constraint and viscous Hamilton-Jacobi equations with unbounded data ⋮ General mean reflected backward stochastic differential equations ⋮ On backward stochastic differential equations and strict local martingales ⋮ BSDEs in utility maximization with BMO market price of risk ⋮ Ong−evaluations with domains under jump filtration ⋮ Anticipated backward stochastic differential equations with quadratic growth ⋮ Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition ⋮ Pseudo linear pricing rule for utility indifference valuation ⋮ Systems of Ergodic BSDEs Arising in Regime Switching Forward Performance Processes ⋮ A simple constructive approach to quadratic BSDEs with or without delay ⋮ OPTIMAL STOCHASTIC CONTROL PROBLEM UNDER MODEL UNCERTAINTY WITH NONENTROPY PENALTY ⋮ A stability approach for solving multidimensional quadratic BSDEs ⋮ Existence and uniqueness results for BSDE with jumps: the whole nine yards ⋮ Anticipated backward SDEs with jumps and quadratic-exponential growth drivers ⋮ 44th seminar on probability. Including papers from the `Journées de Probabilités', Dijon, France, June 2010 ⋮ Backward stochastic differential equations with unbounded generators ⋮ Contracting Theory with Competitive Interacting Agents ⋮ Multidimensional Markovian FBSDEs with super-quadratic growth ⋮ A class of globally solvable Markovian quadratic BSDE systems and applications ⋮ Stochastic control for a class of nonlinear kernels and applications ⋮ Adaptive importance sampling in least-squares Monte Carlo algorithms for backward stochastic differential equations ⋮ Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs ⋮ Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions ⋮ Quadratic BSDEs with mean reflection ⋮ Open-loop equilibrium strategy for mean-variance portfolio problem under stochastic volatility ⋮ Open-loop equilibrium reinsurance-investment strategy under mean-variance criterion with stochastic volatility ⋮ Equilibrium Strategies for Alpha-Maxmin Expected Utility Maximization ⋮ Stability results for martingale representations: The general case ⋮ Quadratic \(G\)-BSDEs with convex generators and unbounded terminal conditions ⋮ Solvability of a class of mean-field BSDEs with quadratic growth ⋮ ROBUST UTILITY MAXIMIZATION IN NONDOMINATED MODELS WITH 2BSDE: THE UNCERTAIN VOLATILITY MODEL ⋮ Quadratic mean-field reflected BSDEs ⋮ Quadratic \(g\)-convexity, \(C\)-convexity and their relationships ⋮ On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions: the critical case ⋮ Numerical simulation of quadratic BSDEs

Cites Work

• On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions
• Adapted solution of a backward stochastic differential equation
• 44th seminar on probability. Including papers from the `Journées de Probabilités', Dijon, France, June 2010
• Backward SDEs with superquadratic growth
• An exponential martingale equation
• Quadratic BSDEs with convex generators and unbounded terminal conditions
• Some new maximal inequalities
• Backward stochastic differential equations with continuous coefficient
• Backward stochastic differential equations and partial differential equations with quadratic growth.
• Quadratic BSDEs driven by a continuous martingale and applications to the utility maximization problem
• BSDE with quadratic growth and unbounded terminal value
• Classical and variational differentiability of BSDEs with quadratic growth
• Solvability of backward stochastic differential equations with quadratic growth
• Utility maximization in incomplete markets
• Dynamic exponential utility indifference valuation
• BSDEs and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations.
• A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem
• Risk-Sensitive Control and an Optimal Investment Model
• Pricing Via Utility Maximization and Entropy
• Backward Stochastic Differential Equations in Finance
• Existence for BSDE with superlinear–quadratic coefficient
• Some New BSDE Results for an Infinite-Horizon Stochastic Control Problem
• The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets
• Stochastic finance. An introduction in discrete time
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Monotone stability of quadratic semimartingales with applications to unbounded general quadratic BSDEs