In the world of reinsurance, accurately determining 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 of worst-case scenarios.

To address this challenge, reinsurers use a variety of traditional measures for evaluating risk, such as Probable Maximum Loss (PML), Value at Risk (VaR), and Tail Value at Risk (TVaR). However, in many instances, it can be very difficult for a reinsurer to measure these risks given the information they have at hand.

As a result, the application of Monte Carlo simulation is being considered more often in order to better prepare a variety of industries for a range of events. 

WHAT IS MONTE CARLO SIMULATION?

For those unfamiliar with the process, Monte Carlo simulation is an analytical technique through which the risk associated with any given venture or project can be evaluated and measured. 

A computerized 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 that 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—and everything in between.  

An example of a reinsurance application of Monte Carlo simulation is its use for catastrophe modeling, 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 explained 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 impact 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 impact on the insured portfolio, risk-transfer effect of reinsurance, the proportion of time reinsurance is exhausted, and other metrics. 

ACCEPTABLE LOSSES

Another example is a recent and very telling study 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.

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, made their predictions by first establishing what level of loss in capital position would be unacceptable. Then, using Monte Carlo simulation with risk-analysis software, they analyzed three variations of an underwriting arrangement. 

For each version of the deal, they ran simulations using log-normal, inverse Gaussian (a two-parameter family of continuous probability distributions) 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 the most profit.  The multiperspective set of risk analyses demonstrated how it is possible to effectively squeeze the riskiness of a deal down to almost nothing.

REAL-WORLD APPLICATIONS

Agricorp, the Ontario, Canada-based government corporation responsible for crop insurance, offers another example of the expansion of Monte Carlo techniques in reinsurance. Agricorp combines Monte Carlo with more than 30 years of data to ensure there is enough funding in reserves to meet possible losses to farmers’ crops due to extreme-weather events. 

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 at a much smaller level than before in order to create sustainable, healthy pricing for these risks. 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 great uncertainty, and Monte Carlo simulation offers a simple-to-use, effective method for being better prepared.