Optimal portfolios under a value-at-risk constraint with applications to inventory control in supply chains

Ka Fai Cedric Yiu, S. Y. Wang, K. L. Mak

Research output: Journal article publicationJournal articleAcademic researchpeer-review

13 Citations (Scopus)


The optimal portfolio problem under a VaR (value at risk) constraint is reviewed. Two different formulations, namely with and without consumption, are illustrated. This problem can be formulated as a constrained stochastic optimal control problem. The optimality conditions can be derived using the dynamic programming technique and the method of Lagrange multiplier can be applied to handle the VaR constraint. The method is extended for inventory management. Different from traditional inventory models of minimizing overall cost, the cashflow dynamic of a manufacturer is derived by considering a portfolio of inventory of raw materials together with income and consumption. The VaR of the portfolio of assets is derived and imposed as a constraint. Furthermore, shortage cost and holding cost can also be formulated as probabilistic constraints. Under this formulation, we find that holdings in high risk inventory are optimally reduced by the imposed value-at-risk constraint.
Original languageEnglish
Pages (from-to)81-94
Number of pages14
JournalJournal of Industrial and Management Optimization
Issue number1
Publication statusPublished - 28 Nov 2008


  • HJB-equation
  • Inventory control
  • Optimal portfolio
  • Value-at-risk

ASJC Scopus subject areas

  • Business and International Management
  • Strategy and Management
  • Control and Optimization
  • Applied Mathematics

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