Utility maximization in an illiquid market in continuous time

H. Mete Soner, Mirjana Vukelja

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

A utility maximization problem in an illiquid market is studied. The financial market is assumed to have temporary price impact with finite resilience. After the formulation of this problem as a Markovian stochastic optimal control problem a dynamic programming approach is used for its analysis. In particular, the dynamic programming principle is proved and the value function is shown to be the unique discontinuous viscosity solution. This characterization is utilized to obtain numerical results for the optimal strategy and the loss due to illiquidity.

Original languageEnglish (US)
Pages (from-to)285-321
Number of pages37
JournalMathematical Methods of Operations Research
Volume84
Issue number2
DOIs
StatePublished - Oct 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)
  • Management Science and Operations Research

Keywords

  • Comparison theorem
  • Hamilton–Jacobi–Bellman equation
  • Liquidity risk
  • Price impact
  • Viscosity solution
  • Weak dynamic programming

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