Pitfalls in the Probability of ruin Type Risk Management

Funding levels for many insurance and financial risk entities are often set to achieve a certain low probability of ruin. Specific real world examples which utilize the same essential methodology include: funding self insurance at a certain percentile of aggregate losses, Value at Risk (VAR) funding of investment banks, return period or PML funding of property catastrophe exposures, and probability of ruin through stochastic modeling commonly used in Europe as in Daykin (1994). We use the concepts of probability of ruin, return period, and percentile interchangeably in this paper. Butsic (1992) has pointed out that these analyses neglect to consider the severity of insolvency. This paper addresses a somewhat related issue. Probability of ruin may often be inconsistent with many other reasonable risk management criteria. For example, combining two independent risks may produce a required funding level at a 1% probability of ruin which is actually higher than the sum of the separate 1% probability of ruin funding levels for each of the risks. Use of this criterion for risk management may lead to the nonsensical result of discouraging risk sharing between independent risks. We examine several examples of this phenomenon and how it may lead to undesirable risk management strategies.