Utility maximization in an illiquid market in continuous time

H. Mete Soner () and Mirjana Vukelja ()
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H. Mete Soner: ETH Zurich
Mirjana Vukelja: ETH Zurich

Mathematical Methods of Operations Research, 2016, vol. 84, issue 2, No 3, 285-321

Abstract: 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.

Keywords: Liquidity risk; Price impact; Weak dynamic programming; Hamilton–Jacobi–Bellman equation; Viscosity solution; Comparison theorem (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s00186-016-0544-2

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