Optimal dividend strategies for a catastrophe insurer
Metadatos:
Mostrar el registro completo del ítemAutor/es:
Azcue, Pablo
Muler, Nora
Albrecher, Hansjörg
Fecha:
2024-06Resumen
In this paper we study the problem of optimally paying out dividends
from an insurance portfolio, when the criterion is to maximize the expected
discounted dividends over the lifetime of the company and the portfolio
contains claims due to natural catastrophes, modelled by a shot-noise Cox claim
number process. The optimal value function of the resulting two-dimensional
stochastic control problem is shown to be the smallest viscosity supersolution of
a corresponding Hamilton-Jacobi-Bellman equation, and we prove that it can
be uniformly approximated through a discretization of the space of the free
surplus of the portfolio and the current claim intensity level. We implement
the resulting numerical scheme to identify optimal dividend strategies for such
a natural catastrophe insurer, and it is shown that the nature of the barrier and
band strategies known from the classical models with constant Poisson claim
intensity carry over in a certain way to this more general situation, leading
to action and non-action regions for the dividend payments as a function of
the current surplus and intensity level. We also discuss some interpretations in
terms of upward potential for shareholders when including a catastrophe sector
in the portfolio.
Este artículo se encuentra originalmente publicado en Frontiers of Mathematical Finance (e-
ISSN:2769-6715)