De Finetti's control problem with Parisian ruin for spectrally negative L\'evy processes
Probability
2019-06-13 v1 Optimization and Control
Abstract
We consider de Finetti's stochastic control problem when the (controlled) process is allowed to spend time under the critical level. More precisely, we consider a generalized version of this control problem in a spectrally negative L\'evy model with exponential Parisian ruin. We show that, under mild assumptions on the L\'evy measure, an optimal strategy is formed by a barrier strategy and that this optimal barrier level is always less than the optimal barrier level when classical ruin is implemented. Also, we give necessary and sufficient conditions for the barrier strategy at level zero to be optimal.
Keywords
Cite
@article{arxiv.1906.05076,
title = {De Finetti's control problem with Parisian ruin for spectrally negative L\'evy processes},
author = {Jean-François Renaud},
journal= {arXiv preprint arXiv:1906.05076},
year = {2019}
}