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Regularity properties in a state-constrained expected utility maximization problem

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  • Mourad Lazgham

Abstract

We consider a stochastic optimal control problem in a market model with temporary and permanent price impact, which is related to an expected utility maximization problem under finite fuel constraint. We establish the initial condition fulfilled by the corresponding value function and show its first regularity property. Moreover, we can prove the existence and uniqueness of optimal strategies under rather mild model assumptions. On the one hand, this result is of independent interest. On the other hand, it will then allow us to derive further regularity properties of the corresponding value function, in particular its continuity and partial differentiability. As a consequence of the continuity of the value function, we will prove the dynamic programming principle without appealing to the classical measurable selection arguments.

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  • Mourad Lazgham, 2015. "Regularity properties in a state-constrained expected utility maximization problem," Papers 1510.03079, arXiv.org.
  • Handle: RePEc:arx:papers:1510.03079
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    File URL: http://arxiv.org/pdf/1510.03079
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    References listed on IDEAS

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    1. Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    2. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    3. Bruno Bouchard & Marcel Nutz, 2011. "Weak Dynamic Programming for Generalized State Constraints," Papers 1105.0745, arXiv.org, revised Oct 2012.
    4. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
    5. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, July.
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