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Multi-dimensional impulse/singular controls and their regularity properties
Probability| Speaker: | Xin Guo, UC Berkeley |
| Location: | 2112 MSB |
| Start time: | Wed, Nov 19 2008, 4:10PM |
Description
Many problems in engineering and economics are formulated in the
impulse/singular control framework. Compared to regular controls,
impulse control provides a more natural mathematical framework when the
state space is discontinuous. However, many structural results amount
to solving complex algebraic equations that are hard to verify without
a priori knowledge of the regularity property, thus the correctness of
the ``solutions'' is dubious. In this talk, we provide sufficient
conditions for the smooth-fit $C1$ property of the value function for
multi-dimensional controlled diffusions, using a viscosity solution
approach. This approach is different from the Quasi-Variational
Inequalities (QVI) established by Bensoussan and Lions (1982). We show
by simple examples where the regularity property may fail especially in
multi-dimensional case.