Reinsurance is the backstop of the insurance industry. Reinsurers underwrite the policies written by insurance companies to protect these companies against losses heavy enough to destabilize them. These deals are a way of sharing risk. This makes reinsurance a business where opportunities must be evaluated with great caution. For this, Monte Carlo simulation is an ideal analytical technique and @RISK an ideal tool. A recent study published by Lina S. Chan, Fellow of the Society of Actuaries and managing partner of CP Risk Solutions, and Domingo Castelo Joaquin, associate professor of finance at Illinois State University, uses @RISK to propose a method for evaluating reinsurance underwriting opportunities and mitigating the risks that accompany them.¹ In their explanations of this method, Chan and Joaquin reveal a good deal about the thinking behind reinsurance strategies.

A Basic Model of Claims Risk and Capital Position
Chan and Joaquin demonstrate the evaluation process using a hypothetical case: Delta Health and Life receives a request for stop-loss proposal from Victory Trust.  Delta’s reinsurance portfolio consists of small policies with low risk exposure, and Victory Trust is the self-insurance vehicle for a major manufacturing conglomerate that underwrites medical insurance for thousands of employees.  What the trust is seeking is a policy that will protect them when they experience claims that are unexpectedly severe. Victory Trust could be a big catch for Delta, but once landed, it could incur losses heavy enough to bring down Delta.  The question Chan and Joaquin use @RISK to address is, “How will reinsuring Victory Trust affect Delta’s capital position?”

The first step for Delta in the process was to analyze medical claim trends among the employees insured by Victory Trust to find out if the proposed premium is enough to cover the unexpected claims, in addition to the known potential claims, a reasonable claim cost fluctuation, administrative expenses, and return on capital.   It is the uncertainty in the size of the stop-loss claims and its impact on Delta’s capital position that is worrisome for Delta’s management.  This is where @RISK comes in.  “Instead of reinventing Monte Carlo simulation within an Excel environment,” Joaquin notes, “one can instead simply load @RISK and focus on model design and analysis. @RISK allows us to use our time more efficiently and more intelligently.”

To gain a balanced perspective on the potential size of the stop-loss claims, Chan and Joaquin created three different @RISK models, based on Victory’s claims history and trend factors. The three models share the same claims frequency distribution (Poisson), but differ in terms of the distribution used to model claim severity.  The simulation is used to assess the probability that Delta’s capital position will be depleted by at least five percent and also the probability that its capital position will improve. The first two models, which employ the log-normal and the inverse Gauss distributions to model claim severity, yielded encouraging results. But the third model, which employs the log-logistic distribution, told a much bleaker story.  Because of this split in possible outcomes and the disproportionate weight Victory Trust would carry in Delta’s portfolio, Chan and Joaquin explored ways by which Delta could transfer some of the risk through reinsurance.

Minimizing Downside Risk
They considered two alternative reinsurance strategies: (1) a 50% quota share reinsurance and (2) an aggregate excess reinsurance combined with a 50% quota share reinsurance. Under the first plan, Delta would share half its premium income and its claims losses with the reinsurer.  Under the second arrangement, in addition to a 50% quota share reinsurance, Delta would be indemnified against aggregate retained loss that exceeds a specified amount, in return for a reinsurance premium.  The combination of 50 percent quota sharing with aggregate excess reinsurance is clearly the most conservative approach. It should diminish downside risk––but then, it would also reduce upside opportunity.

This is, in fact, what the three simulation models revealed.  Under Model 1 and Model 2, the 50 percent quota share scheme resulted in slightly better odds of an improved capital position and lower probabilities of unacceptable losses.  Under Model 3, the 50 percent quota share scheme, while also resulting in minimally better odds of an improved capital position, resulted in a probability of unacceptable losses that was still too high.   However, when the 50 percent quota share was combined with aggregate excess loss coverage, Delta’s capital position ended in safe territory for all three models.

Going Beyond the Numbers
In addition to generating probability estimates, the models developed by Chan and Joaquin provide another avenue to risk mitigation by pinpointing the variables that exert the most powerful influence on ending capital position. In the Delta-Victory Trust case, the models identified claim frequency and claim severity as the most influential variables. This should allow decision makers to focus on policies that address these forces. To be effective, such efforts should address potential agency problems in the contractual relationship between Victory and Delta. Victory is a self-administered trust, and Delta will have to rely on Victory to perform accurate and unbiased administration consistent with guidelines. Together the two insurers need to establish procedures to ensure that this is indeed the case.

1. Lina S. Chan and Domingo Castelo Joaquin, “Using Simulation to Support the Reinsurance Decision of a Medical Stop-loss Provider,” Insurance Markets and Companies: Analyses and Actuarial Computations, 1, 2, 65-77.

» Read the full white paper here
» More information about @RISK