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

2020/07/13 by Renaud, Jean-François, Simard, Clarence · 1 citation
#FOS: Economics and business #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Risk Management (q-fin.RM)

paper · doi:10.48550/arxiv.2007.06330

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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