Robust time-consistent mean-variance portfolio selection problem with multivariate stochastic volatility

被引:13
作者
Yan, Tingjin [1 ]
Han, Bingyan [1 ]
Pun, Chi Seng [2 ]
Wong, Hoi Ying [1 ]
机构
[1] Chinese Univ Hong Kong, Dept Stat, Shatin, Hong Kong, Peoples R China
[2] Nanyang Technol Univ, Sch Phys & Math Sci, Singapore, Singapore
关键词
Time-inconsistency; Dominated model uncertainty; Mean-variance portfolio selection; Stochastic covariance matrix; Principal component stochastic volatility model; Hamilton-Jacobi-Bellman-Isaacs equations; OPTIMAL INVESTMENT; REINSURANCE; OPTIMIZATION; CONSUMPTION; EQUATIONS; INSURERS; RULES; RISK;
D O I
10.1007/s11579-020-00271-0
中图分类号
F8 [财政、金融];
学科分类号
0202 ;
摘要
This paper solves for the robust time-consistent mean-variance portfolio selection problem on multiple risky assets under a principle component stochastic volatility model. The model uncertainty is introduced to the drifts of the risky assets prices and the stochastic eigenvalues of the covariance matrix of asset returns. Using an extended dynamic programming approach, we manage to derive a semi-closed form solution of the desired portfolio via the solution to a coupled matrix Riccati equation. We provide the conditions, under which we prove the existence and the boundedness of the solution to the coupled matrix Riccati equation and derive the value function of the control problem. Moreover, we conduct numerical and empirical studies to perform sensitivity analyses and examine the losses due to ignoring model uncertainty or volatility information.
引用
收藏
页码:699 / 724
页数:26
相关论文
共 38 条
  • [1] Moment explosions in stochastic volatility models
    Andersen, Leif B. G.
    Piterbarg, Vladimir V.
    [J]. FINANCE AND STOCHASTICS, 2007, 11 (01) : 29 - 50
  • [2] A QUARTET OF SEMIGROUPS FOR MODEL SPECIFICATION, ROBUSTNESS, PRICES OF RISK, AND MODEL DETECTION
    Anderson, Evan W.
    Hansen, Lars Peter
    Sargent, Thomas J.
    [J]. JOURNAL OF THE EUROPEAN ECONOMIC ASSOCIATION, 2003, 1 (01) : 68 - 123
  • [3] [Anonymous], 1921, Risk, Uncertainty and Profit
  • [4] Dynamic Mean-Variance Asset Allocation
    Basak, Suleyman
    Chabakauri, Georgy
    [J]. REVIEW OF FINANCIAL STUDIES, 2010, 23 (08) : 2970 - 3016
  • [5] Robust multivariate portfolio choice with stochastic covariance in the presence of ambiguity
    Bergen, V
    Escobar, M.
    Rubtsov, A.
    Zagst, R.
    [J]. QUANTITATIVE FINANCE, 2018, 18 (08) : 1265 - 1294
  • [6] The robust Merton problem of an ambiguity averse investor
    Biagini, Sara
    Pinar, Mustafa C.
    [J]. MATHEMATICS AND FINANCIAL ECONOMICS, 2017, 11 (01) : 1 - 24
  • [7] MEAN-VARIANCE PORTFOLIO OPTIMIZATION WITH STATE-DEPENDENT RISK AVERSION
    Bjoerk, Tomas
    Murgoci, Agatha
    Zhou, Xun Yu
    [J]. MATHEMATICAL FINANCE, 2014, 24 (01) : 1 - 24
  • [8] On time-inconsistent stochastic control in continuous time
    Bjork, Tomas
    Khapko, Mariana
    Murgoci, Agatha
    [J]. FINANCE AND STOCHASTICS, 2017, 21 (02) : 331 - 360
  • [9] Optimal investment for insurers with correlation risk: risk aversion and investment horizon
    Chiu, Mei Choi
    Wong, Hoi Ying
    [J]. IMA JOURNAL OF MANAGEMENT MATHEMATICS, 2018, 29 (02) : 207 - 227
  • [10] Mean-variance portfolio selection with correlation risk
    Chiu, Mei Choi
    Wong, Hoi Ying
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 263 : 432 - 444