Risk Diversifying Treaty Between Two Companies with Only One in Insurance Business

摘要

We consider an insurance company (Company 1) and another company (Company 2) operating under a risk diversification treaty; we assume that Company 2 does not have any insurance business of its own. Company 2 takes care of a pre-agreed fraction of any possible deficit that Company 1 may face; in return, Company 2 gets a retainer fee at a constant rate. (The situation can also be looked upon as Company 1 acting as a subsidiary of Company 2.) The joint dynamics is modelled in terms of appropriate Sko-rokhod problem in the quadrant. Corresponding ruin problem is studied, and advantages of the treaty are pointed out. It is shown that ruin probability decays at a faster rate under the treaty. Some numerical results are also presented to project advantages of our formal model.