摘要：Motivation. An important consideration in a risk transfer analysis is the potential variability of loss timing. By excluding this variability, a risk transfer analysis could lead to materially different results, thereby causing users to draw different conclusions about risk transfer. Method. This paper specifically illustrates the variation in payment patterns commonly found in paid loss and allocated loss adjustment expense development patterns (payment patterns) then provides an example of one method that can be used to model this payment pattern volatility. The impact of modeling this payment pattern volatility is illustrated with Expected Reinsurer Deficit (ERD) results under a hypothetical reinsurance structure. Important model considerations also reflected are correlation and discount rate assumptions. The ERD test is also used to illustrate the sensitivity of these modeled assumptions. Results. The change in the results of a risk transfer test such as the ERD test can be material after consideration of payment pattern timing. Conclusions. Modeling the variation of payment patterns is important for a broad spectrum of actuarial analyses. When evaluating reinsurance risk transfer test statistics it is important to keep in mind features that are sensitive to the variation of loss payment timing. The loss payment timing may have a significant impact on the present value of losses ceded to a reinsurer. At the very least the variation in timing will have an impact on the present value of losses used in the ERD test statistic, particularly with larger discount rates. Correlation of payment timing (or duration) with ultimate loss and allocated loss adjustment expense (ALAE) modeled is also an important consideration that can impact the results of the ERD test. The results below show the sensitivity of changes in correlation and discount rates combined with modeling the variation in the payment timing of ceded paid loss and ALAE
关键词：Risk Transfer; Timing Risk; ERD test; Correlation; Sensitivity of Assumptions
