Dynamic and granular loss reserving with copulae

Abstract

An intensive research sprang up for stochastic methods in insurance during the past years. To meet all future claims rising from policies, it is requisite to quantify the outstanding loss liabilities. Loss reserving methods based on aggregated data from run-off triangles are predominantly used to calculate the claims reserves. Conventional reserving techniques have some disadvantages: loss of information from the policy and the claim's development due to the aggregation, zero or negative cells in the triangle; usually small number of observations in the triangle; only few observations for recent accident years; and sensitivity to the most recent paid claims.To overcome these dilemmas, granular loss reserving methods for individual claim-by-claim data will be derived. Reserves' estimation is a crucial part of the risk valuation process, which is now a front burner in economics. Since there is a growing demand for prediction of total reserves for different types of claims or even multiple lines of business, a time-varying copula framework for granular reserving will be established.

The effect of reinsurance treaties on the cedent loss reserving

“…Their findings showed that the new approach provides more accurate predictions on nonhomogeneous portfolios. Other authors, such as Baudry and Robert (2017), Crevecoeur et al (2019), Duval and Pigeon (2019), Maciak et al (2018), Cedent loss reserving Merz et al (2014), Noviyanti et al (2019), Salzmann and Wüthrich (2012) and Wüthrich (2018), among others, considered a variety of methods, including multivariate models, copula models, machine learning approaches and neural network approaches. The impact of a reinsurance treaty on many actuarial aspects of an insurance company has been studied by many authors.…”