Time-Inconsistent Stochastic Linear-Quadratic Control: Characterization and Uniqueness of Equilibrium

DOI10.1137/15M1019040zbMath1414.91340arXiv1504.01152OpenAlexW3121506041MaRDI QIDQ5346494

Ying Hu, Hanqing Jin, Xun Yu Zhou

Publication date: 24 May 2017

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.01152

zbMATH Keywords

time inconsistencyforward-backward stochastic differential equationmean-variance portfolio selectionstochastic linear-quadratic controluniqueness of equilibrium control

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Optimal stochastic control (93E20) Financial applications of other theories (91G80) Portfolio theory (91G10)

Related Items (78)

Time-consistent mean-variance reinsurance-investment problem with long-range dependent mortality rate ⋮ Non-exponential discounting portfolio management with habit formation ⋮ Time-inconsistent stochastic optimal control problems: a backward stochastic partial differential equations approach ⋮ Equilibrium investment and risk control for an insurer with non-Markovian regime-switching and no-shorting constraints ⋮ Who Are I: Time Inconsistency and Intrapersonal Conflict and Reconciliation ⋮ Characterization of stochastic equilibrium controls by the Malliavin calculus ⋮ A Constructive Approach to Existence of Equilibria in Time-Inconsistent Stochastic Control Problems ⋮ On the Time-Inconsistent Deterministic Linear-Quadratic Control ⋮ Alpha-robust mean-variance reinsurance-investment strategy ⋮ A Nash-Type Fictitious Game Framework to Time-Inconsistent Stochastic Control Problems ⋮ Mean-Variance Portfolio Selection with Dynamic Targets for Expected Terminal Wealth ⋮ Equilibrium pairs trading under delayed cointegration ⋮ Conditional optimal stopping: a time-inconsistent optimization ⋮ Equilibrium and precommitment mean-variance portfolio selection problem with partially observed price index and multiple assets ⋮ Open-loop equilibrium strategy for mean-variance asset-liability management with margin requirements ⋮ Time-inconsistent linear-quadratic non-zero sum stochastic differential games with random jumps ⋮ Time-consistent mean-variance asset-liability management with random coefficients ⋮ Conditional LQ time-inconsistent Markov-switching stochastic optimal control problem for diffusion with jumps ⋮ Stochastic Control of Optimized Certainty Equivalents ⋮ Robust time-inconsistent stochastic linear-quadratic control with drift disturbance ⋮ Open-loop equilibrium strategy for mean-variance asset-liability management portfolio selection problem with debt ratio ⋮ Consistent investment of sophisticated rank‐dependent utility agents in continuous time ⋮ Time inconsistent asset-liability management with partial information ⋮ An extended McKean-Vlasov dynamic programming approach to robust equilibrium controls under ambiguous covariance matrix ⋮ Equilibrium for a time-inconsistent stochastic linear-quadratic control system with jumps and its application to the mean-variance problem ⋮ Uniqueness of equilibrium strategies in dynamic mean-variance problems with random coefficients ⋮ Me, myself and I: a general theory of non-Markovian time-inconsistent stochastic control for sophisticated agents ⋮ Deterministic dynamic Stackelberg games: time-consistent open-loop solution ⋮ Subgame-perfect equilibrium strategies for time-inconsistent recursive stochastic control problems ⋮ A singular linear quadratic time-inconsistent optimal control problem ⋮ Time-inconsistent stochastic linear-quadratic control problem with indefinite control weight costs ⋮ A class of optimal control problems of forward-backward systems with input constraint ⋮ Weak equilibria for time‐inconsistent control: With applications to investment‐withdrawal decisions ⋮ Equilibrium investment with random risk aversion ⋮ Open-loop equilibriums for a general class of time-inconsistent stochastic optimal control problems ⋮ Time-Inconsistent Recursive Stochastic Optimal Control Problems ⋮ A class of non-zero-sum stochastic differential games between two mean–variance insurers under stochastic volatility ⋮ Robust equilibrium strategies for time-inconsistent stochastic optimal control problems with applications ⋮ Time-inconsistent LQ games for large-population systems and applications ⋮ Portfolio selection with exploration of new investment assets ⋮ Nonlocality, nonlinearity, and time inconsistency in stochastic differential games ⋮ Investment-consumption-insurance optimisation problem with multiple habit formation and non-exponential discounting ⋮ Non-Markovian mean-variance portfolio selection problems via closed-loop equilibrium strategies ⋮ Open-loop equilibrium strategy for mean-variance portfolio selection with investment constraints in a non-Markovian regime-switching jump-diffusion model ⋮ Mean-variance asset-liability management under CIR interest rate and the family of 4/2 stochastic volatility models with derivative trading ⋮ On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems ⋮ A stochastic linear-quadratic differential game with time-inconsistency ⋮ Optimal feedback controls of stochastic linear quadratic control problems in infinite dimensions with random coefficients ⋮ Mean-Variance Portfolio Selection for Partially Observed Point Processes ⋮ Time-consistent investment-proportional reinsurance strategy with random coefficients for mean-variance insurers ⋮ Equilibrium controls in time inconsistent stochastic linear quadratic problems ⋮ Characterizations of closed-loop equilibrium solutions for dynamic mean-variance optimization problems ⋮ On the Equilibrium Strategies for Time-Inconsistent Problems in Continuous Time ⋮ Extended backward stochastic Volterra integral equations and their applications to time-inconsistent stochastic recursive control problems ⋮ Continuous-time mean-variance portfolio selection with regime-switching financial market: time-consistent solution ⋮ Robust time-consistent mean-variance portfolio selection problem with multivariate stochastic volatility ⋮ A non-exponential discounting time-inconsistent stochastic optimal control problem for jump-diffusion ⋮ Open-loop equilibrium strategy for mean-variance portfolio problem under stochastic volatility ⋮ Open-loop equilibrium strategy for mean-variance portfolio selection: a log-return model ⋮ Time-consistent longevity hedging with long-range dependence ⋮ Robust time-inconsistent stochastic control problems ⋮ Open-loop equilibrium reinsurance-investment strategy under mean-variance criterion with stochastic volatility ⋮ Portfolio choice with skewness preference and wealth-dependent risk aversion ⋮ Small-time solvability of a flow of forward-backward stochastic differential equations ⋮ Robust state-dependent mean-variance portfolio selection: a closed-loop approach ⋮ Time-Inconsistent Linear Quadratic Optimal Control Problems for Stochastic Evolution Equations ⋮ Time consistent mean-variance asset allocation for a DC plan with regime switching under a jump-diffusion model ⋮ Dynamic portfolio choice without cash ⋮ Mean-Variance Portfolio Selection under a Non-Markovian Regime-Switching Model: Time-Consistent Solutions ⋮ Time-Inconsistent Consumption-Investment Problems in Incomplete Markets under General Discount Functions ⋮ CONTINUOUS-TIME MEAN–VARIANCE OPTIMIZATION FOR DEFINED CONTRIBUTION PENSION FUNDS WITH REGIME-SWITCHING ⋮ Controlled Markov chains with non-exponential discounting and distribution-dependent costs ⋮ Time-inconsistent stochastic optimal control problems and backward stochastic volterra integral equations ⋮ Characterizations of equilibrium controls in time inconsistent mean-field stochastic linear quadratic problems. I ⋮ Optimal control of an objective functional with non-linearity between the conditional expectations: solutions to a class of time-inconsistent portfolio problems ⋮ Closed-Loop Equilibrium for Time-Inconsistent McKean--Vlasov Controlled Problem ⋮ Mean-variance portfolio selection with non-negative state-dependent risk aversion ⋮ Time-Consistent Investment and Reinsurance Strategies for Mean–Variance Insurers in N-Agent and Mean-Field Games

Cites Work

• A theory of Markovian time-inconsistent stochastic control in discrete time
• Investment and consumption without commitment
• Multiple solutions under quasi-exponential discounting
• Continuous exponential martingales and BMO
• Time-inconsistent optimal control problems and the equilibrium HJB equation
• The golden rule when preferences are time inconsistent
• Time-consistent mean-variance portfolio selection in discrete and continuous time
• Time-Inconsistent Stochastic Linear--Quadratic Control
• A General Stochastic Maximum Principle for Optimal Control Problems
• MEAN–VARIANCE PORTFOLIO OPTIMIZATION WITH STATE‐DEPENDENT RISK AVERSION
• Unnamed Item
• Unnamed Item

This page was built for publication: Time-Inconsistent Stochastic Linear-Quadratic Control: Characterization and Uniqueness of Equilibrium