The first paper in this series discussed the impact that loss volatility has on the risk finance decision-making process, and the second paper explored the notion of loss dependence and the influence of interdependencies between sources of corporate risk. In this third installment in our Alternative Risk series, we build on these concepts and discuss the mapping of retained volatility levels to corporate risk appetite in a multiple risk setting. This process is illustrated through the design of an optimized insurance program structure, where stochastic loss models are coupled with market intelligence to perform a risk versus reward trade-off analysis.

• White Paper 1: Beyond Expected Value – Considering Volatility
• White Paper 2: Loss Dependence – A Portfolio Level View of Retained Exposure
• White Paper 3: Corporate Risk Appetite and Program Structuring

Case Study Overview

As in the prior papers, we will focus on a simplified setting in which a fictitious organization (Company ABC) is exposed to several sources of risk. Risk X and Risk Y are each associated with high frequency and moderate severity losses, similar to those often observed in some casualty lines of business. Risk Z is subject to the low frequency and high severity types of losses typically observed in catastrophic perils. In this simple world, insurance policy structures available in the market are also limited. For Risk X and Risk Y, respectively, the policy types available are guaranteed cost and per occurrence deductible options at $1M, $2M or $3M. For Risk Z, the market is offering policies with per occurrence deductibles of $50M, $70M and $90M. Management at Company ABC is somewhat averse to fully self-insuring Risks X and Y. They will not consider fully self-insuring Risk Z due to its catastrophically driven hazard profile.

In this world, realistic stochastic models exist for each of the three sources of risk, and output from them can be tailored to describe the distribution of Company ABC’s retained exposure given a selected retention level. A summary of the monoline retained loss model estimates, rounded to the nearest million, is included in the following table.

Jason Flaxbeard

Alternative Risk Leader

Andrew Golub

Chief Innovation and Analytics Officer

Scott Hornyak

Chief Actuary