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A stochastic control problem with linearly bounded control rates in a Brownian model

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  • Jean-Franc{c}ois Renaud
  • Clarence Simard

Abstract

Aiming for more realistic optimal dividend policies, we consider a stochastic control problem with linearly bounded control rates using a performance function given by the expected present value of dividend payments made up to ruin. In a Brownian model, we prove the optimality of a member of a new family of control strategies called delayed linear control strategies, for which the controlled process is a refracted diffusion process. For some parameters specifications, we retrieve the strategy initially proposed by Avanzi & Wong (2012) to regularize dividend payments, which is more consistent with actual practice.

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  • Jean-Franc{c}ois Renaud & Clarence Simard, 2020. "A stochastic control problem with linearly bounded control rates in a Brownian model," Papers 2007.06330, arXiv.org.
    • Handle: RePEc:arx:papers:2007.06330
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    File URL: http://arxiv.org/pdf/2007.06330
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