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Applications of stochastic control to real options and to liquidity risk model.

Abstract : We study stochastic control applications to real options and to liquidity risk model. More precisely, we investigate, in the first part, a model of optimal portfolio selection under liquidity risk and price impact, then, in the second part, two real option problems: an optimal switching problem and a mixed singular/switching control problem for a dividend policy with reversible investment, and finally, in the third part, a competitive market equilibrium problem under asymmetric information. In the resolution of these problems, stochastic control techniques will be intensively used. The typical approach consists in expressing the dynamic programming principle related to each case, in order to obtain a PDE characterization of the value functions. Based on this approach, we show, in the liquidity risk problem and both real options, that the corresponding value functions are unique solution to the associated system of HJB variational inequalities. In each problem of the first two parts, we obtain the solutions, in particular the optimal control, either explicitly or via an iterative method.
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Contributor : Vathana Ly Vath <>
Submitted on : Monday, December 11, 2006 - 10:20:21 PM
Last modification on : Wednesday, December 9, 2020 - 3:11:25 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 7:19:42 PM


  • HAL Id : tel-00119754, version 1


Vathana Ly Vath. Applications of stochastic control to real options and to liquidity risk model.. Mathematics [math]. Université Paris-Diderot - Paris VII, 2006. English. ⟨tel-00119754⟩



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