Continuous time mean-variance portfolio optimization through the mean field approach

DOI10.1051/ps/2016001zbMath1354.91143OpenAlexW2474074729MaRDI QIDQ2954223

Markus Fischer, Giulia Livieri

Publication date: 12 January 2017

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/11577/3195199

zbMATH Keywords

optimal controldynamic programminglaw of large numbersportfolio optimizationtime inconsistencymean-variance criterionMcKean-Vlasov limit

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Dynamic programming in optimal control and differential games (49L20) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Portfolio theory (91G10)

Related Items (13)

Extended mean field control problem: a propagation of chaos result ⋮ Linear quadratic mean field social optimization: Asymptotic solvability and decentralized control ⋮ Bellman equation and viscosity solutions for mean-field stochastic control problem ⋮ Well-posedness and propagation of chaos for McKean-Vlasov equations with jumps and locally Lipschitz coefficients ⋮ Limit Theory for Controlled McKean--Vlasov Dynamics ⋮ Interbank lending with benchmark rates: Pareto optima for a class of singular control games ⋮ Portfolio diversification and model uncertainty: A robust dynamic mean‐variance approach ⋮ Conditional McKean-Vlasov SDEs with jumps and Markovian regime-switching: wellposedness, propagation of chaos, averaging principle ⋮ A general stochastic maximum principle for mean-field controls with regime switching ⋮ A Mean-Variance Approach to Capital Investment Optimization ⋮ Robust Markowitz mean‐variance portfolio selection under ambiguous covariance matrix ⋮ Linear feedback of mean-field stochastic linear quadratic optimal control problems on time scales ⋮ McKean–Vlasov Optimal Control: Limit Theory and Equivalence Between Different Formulations

Cites Work

• Linear-quadratic mean field games
• Control of McKean-Vlasov dynamics versus mean field games
• A theory of Markovian time-inconsistent stochastic control in discrete time
• A maximum principle for SDEs of mean-field type
• Multiperiod mean-variance portfolio optimization via market cloning
• A general stochastic maximum principle for SDEs of mean-field type
• Forward-backward stochastic differential equations and controlled McKean-Vlasov dynamics
• Continuous-time mean-variance portfolio selection: a stochastic LQ framework
• Controlled Markov processes and viscosity solutions
• Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation
• MEAN–VARIANCE PORTFOLIO OPTIMIZATION WITH STATE‐DEPENDENT RISK AVERSION
• A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS

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