TITLE:
Dividends and Dynamic Solvency Insurance in Two-Dimensional Risk Models
AUTHORS:
Cristina Gosio, Ester C. Lari, Marina Ravera, Maria-Laura Torrente
KEYWORDS:
Two-Dimensional Risk Models, Dynamic Solvency Insurance, Dividends, Reflecting Barriers, Integro-Differential Equations
JOURNAL NAME:
Modern Economy,
Vol.9 No.12,
December
13,
2018
ABSTRACT: In this paper we consider two-dimensional risk models
where the claim counting processes of the two classes of business are assumed
to be Poisson processes. We assume that the dividends are paid because of the
presence of a reflecting upper barrier. Furthermore, in order to avoid ruin, we
consider dynamic solvency insurance contracts that depend on two different
definitions of time of ruin. We present a rather general model and, under
different assumptions, we obtain the equations fulfilled by the discounted
dividend payments and by the net single premium of dynamic solvency insurance.
We also derive some boundary conditions and provide explicit solutions for some
special cases.