The growing trend of Monte Carlo simulation for reinsurance by Randy Heffernan, Head of  Marketing, Palisade Corp
In the world of reinsurance, awareness of risk is critical. Reinsurance policies are typically taken out on the largest of risks, those that are too big for an individual insurance company to handle alone. Risk embodies the very nature of the business, and actuaries who work in reinsurance must therefore be extremely well-versed in the quantification and mitigation of risk.
To address this challenge, reinsurers use a variety of traditional measures for evaluating risk, such as the probable maximum loss (PML), value at risk (VaR), and Tail VaR (TVAR). However, in many instances, it can be very difficult for a reinsurer to measure these risks given the information they have available.
As a result, the application of Monte Carlo simulation is being considered more and more in order to be better prepared for a variety of events in a range of industries. The reinsurance industry has endured numerous larger than expected losses in the last decade or so – everything from Hurricane Katrina to the global financial crisis to the Japanese earthquakes. Perhaps spurred by these losses, the world of reinsurance is looking at different ways of thinking about risk and how to manage it.
What is Monte Carlo simulation?
For those unfamiliar with the technique, Monte Carlo simulation is an analytical technique by which to evaluate and measure the risk associated with any given venture or project. A computerised mathematical technique that allows people to account for risk in quantitative analysis and decision making, Monte Carlo simulation offers the decision-maker a range of possible outcomes and the probabilities they will occur, making it well-suited for underwriting, reserves estimation, and premium pricing exercises. It can show the extreme possibilities – outcomes for the most risky and the most conservative – along with everything in between.
Monte Carlo simulation and catastrophes
An example of a reinsurance application of Monte Carlo simulation is its use for catastrophe modelling, as explored in a recent paper by Enrique de Abla at the University of Waterloo, Jesús Zúñiga of GNP Insurance Mexico, and Marco A. Ramírez Corzo. The researchers explain how Monte Carlo simulation is particularly effective in situations where sufficient data is lacking to compute traditional insurance risk measures. Earthquakes and hurricanes are two such situations. The interactions between the physical processes in these catastrophes are extremely complex, making their impacts very difficult to assess. Using Monte Carlo simulation, the researchers are better able to measure the effect of a complex reinsurance scheme on the risk profile of an insurance company. They are able to compute the pure risk premium, PML, impact on the insured portfolio, risk transfer effect of reinsurance, proportion of time reinsurance is exhausted, and other metrics.
A study of assumptions in reinsurance
Another example is a recent and very telling study by two actuarial in the United States. Lina Chan and Domingo Joaquin sought to predict how a stop-loss underwriting opportunity would affect a reinsurer’s bottom line (http://www.palisade.com/cases/ReinsuranceStopLoss.asp). Chan, a managing partner in CP Risk Solutions and a fellow of the Society of Actuaries, and Joaquin an associate professor of finance at Illinois State University, created their predictions by first establishing what level of loss in capital position would be unacceptable. Then, using Monte Carlo simulation with @RISK in Excel, they analysed three variations of an underwriting arrangement. For each version of the deal, they ran simulations using log-normal, inverse Gaussian, and log-logistic probability functions. There were surprising differences in the researchers’ simulation results. By far the gloomiest outlook was obtained using the log-logistic function, which prompted Chan and Joaquin to endorse the reinsurance deal involving the most sharing of risk, and not least profit. Most striking however, was the possible courses of action that could have resulted from the analysts’ reliance on only one probability function. The multi-perspective set of risk analyses demonstrated how it is possible to effectively squeeze the riskiness of a deal down to almost nothing.
Monte Carlo simulation in crop reinsurance in Ontario
Agricorp, the government corporation in Ontario, Canada responsible for crop insurance, brings us another example of the expansion of Monte Carlo techniques in reinsurance. Agricorp combines Monte Carlo in @RISK with over 30 years of data to ensure there is enough funding in reserves to meet possible losses to farmers’ crops due to extreme weather events. Monte Carlo enables them to examine a range of loss ratios for any given insured event.
Monte Carlo and social reinsurance
Furthermore, a recent report from the World Bank explores the topic of “social reinsurance,” or reinsurance for micro-insurers working with small, impoverished communities in developing nations. Monte Carlo simulation is used for the traditional application of premium pricing, but is being done at a much smaller level than before in order to create sustainable health financing. Similar to the trend of microfinance, Monte Carlo for social reinsurance applies big money analytics at small money levels.
Reinsurance is the backstop of the insurance industry, and a business where opportunities – and pitfalls - should be evaluated with great caution. There has never been a more pressing time for the reinsurance industry to look for better decision making under uncertainty, and Monte Carlo simulation offers a simple-to-use, effective method for being better prepared.
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