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Discussion on a class of impulse consumption control strategy of optimal stochastic problem. (Chinese. English summary) Zbl 1221.93275

Summary: A stochastic control problem is discussed. The impulse consumption control strategy of the problem is governed by a mixed process-geometrical Brownian motion and a Poisson process. In order to achieve the maximum of the objective function defined by the expectation of a utility function, by using the variational inequalities and stochastic calculus control theory, the optimal consumption strategy and the theorem that the optimal value function satisfy are obtained. Furthermore, its numerical computation results for some explicit parameters are calculated.

MSC:

93E20 Optimal stochastic control
49J40 Variational inequalities
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