Analysis of some strategic MAP PH risk models

Abstract

The insurer s surplus is modelled via stochastic processes after the exposition of newlinea Swedish actuary Filip Lundberg: On the theory of risk presented at the VI newlineInternational Congress of Actuaries, 1909. In risk theory, the Cramér-Lundberg risk newlinemodel realises the insurer s surplus for a general insurance business, for which on newlineone side the claims arriving via Poisson process accompanying independent and newlineidentically distributed amount sizes due, and on the other side receiving premiums at newlinea constant rate, setting a positive security loading, with an objective to settle claims. newlineThe risk model is kept back (by both academicians as well as practitioners) as a newlineskeleton framework to test-run numerous financial and corporate strategies, to deal newlinewith the probability of an insurer s ruin and other strategic indicators. newlineLike in any other business, an insurance firm is an establishment with many offices newlinespread across different territories. It possesses a number of policyholders registered newlinefrom several categories. Moreover, government regulations will consistently alter newlinedue to its federal demands. These environmental changes are classified through these newlineoffices, territories, categories and regulations. They are modelled using processes newlinefeaturing a mixture of phases, essentially each having parameters distinct from newlineone another, focusing the impacts of a particular environment. Claims reported newlinein an insurance portfolio will thus have a lump sum form generated through these newlinemulti-phase environments. Hence the Cramér-Lundberg model, since it realises the newlineaggregate claims through a single-phase process, is a loose recorder to fetch the newlineactual volatility of cash outflow in an insurance portfolio. newlineOn a distinct note, the income of an insurer can be highly volatile. Taking cases newlineof firms from developing countries or looking at start-up firms, one can observe that newlinethe volatility in asset portfolio is higher due to the larger variations in the number ofclients, and the distribution of value on their bonds and investments. newline