Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (2): 483-490.doi: 10.1016/S0252-9602(11)60249-X

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OPTIMAL PORTFOLIO ON TRACKING THE EXPECTED WEALTH PROCESS WITH LIQUIDITY CONSTRAINTS

 LUO Kui, WANG Guang-Ming, HU Yi-Jun   

  1. Industrial Training Centre, Shenzhen Polytechnic, Shenzhen 518055, China; China Merchants Bank, Shenzhen 518040, China; School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2008-06-08 Revised:2009-08-20 Online:2011-03-20 Published:2011-03-20
  • Supported by:

    Supported in part by the National Natural Science Foundation of China (10671149) and the Ministry of Education of China (NCET-04-0667)

Abstract:

In this article, the authors consider the optimal portfolio on tracking the expected wealth process with liquidity constraints. The constrained optimal portfolio is first formulated as minimizing the cumulate variance between the wealth process and the expected wealth process. Then, the dynamic programming methodology is applied to reduce the whole problem to solving the Hamilton-Jacobi-Bellman equation coupled with the liquidity constraint, and the method of Lagrange multiplier is applied to handle the constraint. Finally, a numerical method is proposed to solve the constrained HJB equation and the constrained optimal strategy. Especially, the explicit solution to this optimal
problem is derived when there is no liquidity constraint.

Key words: Portfolio selection, wealth tracking, liquidity constraints, HJB equation, Lagrange multiplier

CLC Number: 

  • 91B28
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