# Stochastic Claims Reserving Manual: Advances In Dynamic Modeling

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### Stochastic Claims Reserving Manual: Advances in Dynamic Modeling

Mario V. Wuthrich

RiskLab, ETH Zurich; Swiss Finance Institute

Michael Merz

University of Hamburg

August 21, 2015

Swiss Finance Institute Research Paper No. 15-34

Abstract:

These notes are strongly motivated by practitioners who have been seeking for advise in stochastic claims reserving modeling under Solvency 2 and under the Swiss Solvency Test. There have been tremendous developments since the publication of our first book Stochastic Claims Reserving Methods in Insurance in 2008. Particularly the new solvency guidelines have added a dynamic component to claims reserving which has not been present before. This new viewpoint has motivated numerous new developments, for instance, the claims development result and the risk margin were introduced. The present text considers these new aspects, not treated in our previous book, and it should be viewed as completion to our first book.

### Stochastic Claims Reserving Manual: Advances in Dynamic Modeling – Introduction

Chapter 1 – Claims Reserving Problem

A main feature in non-life insurance is that insurance claims cannot be settled immediately at occurrence. Usually, there is delay in reporting of claims and there is delay in settlement of claims. We describe reasons for such reporting and settlement delays in the next section. As a consequence of these delays we need to predict future cash flows of claims that have occurred in the past and are only settled in the future. These predictions then constitute the basis for pricing of future insurance contracts. This task of prediction is known as the claims reserving problem and it assesses outstanding loss liabilities of past claims. The prediction of these outstanding loss liabilities provide the claims reserves. Importantly, these claims reserves are the largest position on the liability side of the balance sheet of a typical non-life insurance company, see Table 1.1 for an example, and they are essential for the financial strength of the company. Therefore, we aim at describing the claims reserving process in careful detail and we also would like to assess the uncertainties involved in this prediction problem.

1.1 Outstanding loss liabilities

A claim in non-life insurance is triggered by an accident which is an event that causes (financial) damage covered by an insurance contract. The date of claims occurrence is called accident date T1. Typically, time elapses until such a claim is in the administrative system of the insurance company and is available for statistical analysis. The time lag between the accident date and the registration at the insurance company is called reporting delay and the date of registration is termed reporting date T2.

Figure 1.1: Non-life insurance run-off showing the period insured [U1, U2] and a claim with accident date T1 2 [U1, U2], reporting date T2 > U2 and settlement date (claims closing date) T3 > T2. Moreover, we have claims payments (cash flows) during the settlement period [T2, T3].

The reporting delay can be small, say days, but it can also be very large, for example several years. Reasons for such reporting delays are that claims are not reported immediately to the insurance company, for instance, a stolen bike is only reported once it is clear that it will not “reoccur”, but of course the accident date is the day the bike got stolen. Large reporting delays are often caused by claims that cannot be noticed immediately. A common example is an asbestos claim which is usually caused a long time before cancer is diagnosed and reported. The accident date refers to the event when there was contact with asbestos, the trigger of the cancer, and not to the date of the breakout of the asbestos disease.

Once a claim is reported to the insurance company, typically, it cannot be settled immediately. The insurance company starts an investigation, observes the recovery process, waits for external information, external bills, court decisions, etc. This process may last for several years for more involved claims. Of course, the insurance company cannot wait with claims payments until there is a final assessment of the claim but it will continuously pay for justified claims benefits. Therefore, insurance claims trigger a whole sequence of cash flows after the reporting date T2. This second period is called settlement period and the final assessment of a claim is called settlement date or claims closing date T3.

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