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

I. Venkat Appal Raju () and S. Ramasubramanian ()
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I. Venkat Appal Raju: Indian Institute of Technology Jodhpur
S. Ramasubramanian: Indian Statistical Institute

Sankhya B: The Indian Journal of Statistics, 2016, vol. 78, issue 2, No 1, 183-214

Abstract: Abstract 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 Skorokhod 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.

Keywords: Skorokhod problem; Reflected process; Ruin; Ruin probability; Capital injection; Renewal-risk model; Cramer-Lundberg model; Lundberg adjustment coefficient; Light-tailed distribution; Subexponential distribution; Primary 91B30; Secondary 91B70; 60K10; 62P05 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13571-015-0113-3

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