Abstract
The value of a position in a risky asset when optimally sold in an illiquid market is considered. The optimization problem is described as a stochastic impulse control problem, and it is shown that it is related to solving a system of quasi-variational inequalities. Existence of a solution to these inequalities are proved. A numerical implementation of the valuation algorithm is discussed and two numerical examples are presented. Further, two examples where the stochastic impulse control problem can be reduced to deterministic optimization problems are also given.
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