On rational pricing for a profit-seeking insurer in the year of hard market

The aim of this paper is to examine rational pricing of a profit-seeking insurer carrying on its business when underwriting cycle is in its upper phase. We focus on migration of insureds wishing to get the same services at a lower price. We investigate pricing which maximizes the insurer's intrinsic value linked to its attractiveness for investors, provided that its solvency position is fixed. The main tool in this paper is explicit bounds on ruin capital in Lundberg risk model with migration. Written in terms of elementary functions, they make the solution straightforward.