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Selected Development Project
 
Project Title

Mean-variance portfolio selection and asset-liability management with the Wishart process

均值方差投資組合與資產負債管理---威夏爾特過程之情況

 
Principal Investigator Dr CHIU Mei Choi
 
Area of Research Project
Economics
 
Project Period
From 08/2013 To 01/2017
Objectives
  • Developing theories for portfolio policy using the mean-variance (MV) criteria when the financial assets follow the Wishart affine stochastic covariance (WASC) process.
  • Proving the feasibility, optimality and uniqueness of the solution using the backward stochastic differential equation (BSDE) theory.
  • Deriving the HJB equation for the time-consistent MV problem under WASC process
  • Proposing and conducting corresponding numerical studies.
Methods Used

The key research methods are the BSDE theory, martingale approach and HJB equations
Summary of Findings
  • The MV optimal trading strategy is developed under WASC process.
  • The analytical form of MV-efficient frontier under WASC process is obtained.
  • For another utility maximization problem, expected constant-relative-risk-averse (CRRA) is consider as a utility function. The optimal investment policy is obtained under CRRA utility with stochastic interest rate following the extended CIR model, which is the one-dimensional case of WASC process.
Impact
  • As traditional MV approach only considers constant correlations, this project provides the first mathematical result to support empirical findings in the finance literature.
  • In addition, the obtained mathematical method is novel and is expected to be useful in studying linear-quadratic stochastic optimal control problems with unbounded random coefficients in other areas such as engineering and information technology.
Output
There are five acceptance papers:
  • Chiu, M.C., Wong, H.Y. & Zhao J. (2015). Commodity derivatives pricing with cointegration and stochastic covariances. European Journal of Operational Research, 246(2), 476-486.
  • Chiu, M.C., & Wong, H.Y. (2014). Mean-variance asset-liability management with asset correlation risk and insurance liabilities. Insurance: Mathematics and Economics, 59, 300-310.
  • Chiu, M.C., & Wong, H.Y. (2014). Optimal investment for insurers with the extended CIR interest rate model. Abstract and Applied Analysis, (2014) Article ID 129474, 1-12.
  • Chiu, M.C., & Wong, H.Y. (2014). Mean-variance portfolio selection with correlation risk. Journal of Computational and Applied Mathematics, 263, 432-444.
  • Wong, T.W., Chiu, M.C., Wong, H.Y. (2014). Time-consistent mean-variance hedging of longevity risk: Effect of cointegration. Insurance: Mathematics and Economics, 56, 56-67.
Biography of Principal Investigator
Mei Choi obtained her BSc degree in Mathematical Sciences from Hong Kong Baptist University, MPhil degree in Mathematics from Hong Kong University of Science and Technology (HKUST), and PhD degree in Systems Engineering and Engineering Management (SEEM) from the Chinese University of Hong Kong (CUHK). Her work experience includes postdoctoral fellowship at SEEM of CUHK, research associate at Department of Statistics of CUHK, visiting scholar at Department of Mathematics of HKUST, and part-time consultant for the MSc degree program in Financial Mathematics and Statistics of HKUST.
Funding Source

Early Career Scheme