2018/04/07 by Pablo Azcue, Azcue, Pablo, Nora Muler +1 · 2 citations
Social Sciences · Economics, Econometrics and Finance · #Insurance, Mortality, Demography, Risk Management #Stochastic processes and financial applications #Insurance and Financial Risk Management
paper · pdf · doi:10.48550/arxiv.1804.02547
In this paper we study the problem of optimal dividend payment strategy which\nmaximizes the expected discounted sum of dividends to a multidimensional set up\nof n associated insurance companies where the surplus process follows an\nn-dimensional compound Poisson process. The general manager of the companies\nhas the possibility at any time to exercise an irreversible switch into another\nregime; we also take into account an expected discounted value at ruin. This\nmultidimensional dividend problem is a mixed singular control/optimal problem.\nWe prove that the optimal value function is a viscosity solution of the\nassociated HJB equation and that it can be characterized as the smallest\nviscosity supersolution. The main contribution of the paper is to provide a\nnumerical method to approximate (locally uniformly) the optimal value function\nby an increasing sequence of sub-optimal value functions of admissible\nstrategies defined in an n-dimensional grid. As a numerical example, we present\nthe optimal time of merger for two insurance companies.\n