Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework

By Xun Yu Zhou, Duan Li. 2000

1,086 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/bec3d9335aa81eac0fb660e5f00254cfc21c0ded

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Citations in the corpus

Thou shalt buy and hold (2008, background): “The continuous-time Markowitz model (Richardson 1989 , Zhou and Li 2000 ) or the recent behavioural portfolio selection model (Jin and Zhou 2008 ) both lead to similar continuously rebalancing optimal portfolios, even in the Black–Scholes case where there is only one stock available.”
Controlled diffusion processes (2005, background): “) An alternative ‘meanvariance’ formulation in the spirit of Markowitz seeks to maximize a linear combination of the mean and negative variance of X(T ) [119].”
Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns (2015, background): “Zhou and Li[30](2000) transformed the meanvariance problem into a linear quadratic problem and many recent literatures are based on this procedure.”
Paris-Princeton Lectures on Mathematical Finance 2002 (2003, methodology): “To the best of our knowledge, Zhou and Li (2000) were the first to use the embedding technique and linear-quadratic (LQ) optimal control theory to solve the continuous-time meanvariance problem with assets having deterministic diusion coecients.”
Optimal trade execution: A mean quadratic variation approach (2012, methodology): “In [12], the pre-commitment optimal mean-variance policy is determined by formulating the problem in terms of a related Linear-Quadratic (LQ) objective function [ 23 , 15].”
Dynamic Mean-Variance Portfolio Selection with No-Shorting Constraints (2001, methodology): “, [2, 3, 21, 34]), and this in turn provides a powerful tool for solving some finance problems that are linear-quadratic in nature [19, 22, 37].”
Recent advances in reinforcement learning in finance (2021, methodology): “The same approach was then used to solve the continuous-time mean-variance problem [265].”
Numerical Methods for Nonlinear PDEs in Finance (2012, background): “This can be avoided with the help of the results in [18, 28]: Theorem 1 (Equivalent Linear Quadratic (LQ) problem).”
Optimal mean-variance portfolio selection (2016, neutral): “In particular, the results of [10] and [24] do not establish the existence of statically optimal controls in the problems (2.”
Mean-Variance Policy for Discrete-time Cone Constrained Markets: The Consistency in Efficiency and Minimum-Variance Signed Supermartingale Measure (2014, positive): “The derived dynamic optimal investment policy in Li and Ng (2000) and Zhou and Li (2000) is termed by Basak and Chabakauri (2010) as pre-committed dynamic optimal investment policy, as the (adaptive) optimal policy is fixed at time 0 to achieve overall optimality for the entire investment horizon.”