The chain-ladder (CL) method is the most widely used claims reserving technique in non-life insurance. This manuscript introduces a novel approach to computing the CL reserves based on a fundamental restructuring of the data utilization for the CL prediction procedure. Instead of rolling forward the cumulative claims with estimated CL factors, we estimate multi-period factors that project the latest observations directly to the ultimate claims. This alternative perspective on CL reserving creates a natural pathway for the application of machine learning techniques to individual claims reserving. As a proof of concept, we present a small-scale real data application employing neural networks for individual claims reserving.
About a decade ago, research of individual claims reserving utilizing machine learning (ML) techniques began to emerge. Since then, numerous methods and models have been proposed, including regression trees, gradient boosting machines, and neural networks. Nevertheless, the area of individual claims reserving remains predominantly a research domain and has not yet achieved a widespread adoption in industry practice. Schneider-Schwab [18] write: "Typically, newer models which consider richer data on individual claims are either parametric or use machine learning techniques. However, none have become a gold standard, and advances are still needed." We attribute this fact to various challenges. First, it is difficult to find publicly available individual claims data. This clearly hinders research in this area of actuarial science. Second, individual claims data is censored, low-frequency and of a complex time-series structure. It is generally difficult to build good predictive models for such problems. Third, the claims reserving problem is a multi-period forecasting problem. However, often, the underlying algorithms are only trained for performing one-period ahead forecasts. Naturally, a tweak is required to work around this problem going from one-to multi-period forecasts. Fourth, the implementation and structure of the proposed individual claims reserving methods is rather complex and often specific to a certain claims reserving situation, for instance, every insurance company collects historic data of a slightly different nature (and format). This makes it difficult to benchmark the different methods. Moreover, the proposed approaches often need extended hyper-parameter tuning, e.g., to avoid biases, this leaves the question open whether the proposed method easily generalizes to other claims reserving situations (in a broader sense). This paper introduces a fundamentally novel approach which we envision as a transformative step toward the widespread adoption of individual claims reserving across the insurance industry. This transformative step is not about a specific ML architecture, but our core idea is to reorganize historical individual claims data for direct multi-period forecasting. The main step is to reformulate the foundational chain-ladder (CL) reserving algorithm so that one can perform multi-period model fitting and forecasting. Once this step is fully understood, adapting this idea to ML methods is straightforward. We will explain this in detail, after outlining the present state of the field of individual claims reserving using ML methods.
We observe four main techniques to cope with the multi-period forecasting problem in individual claims reserving:
(1) The multi-period forecasting is performed by a recursive one-period forecast procedure using past observations as inputs. Rolling this recursive procedure into the future, missing observed inputs are replaced by their forecasts. This is the first and most popular method used for multiperiod forecasting; for literature in individual claims reserving see, e.g., De Felice-Moriconi [5] and Chaoubi et al. [4]. We briefly explain why this procedure may be problematic. However, in general, this proposal of multi-period forecasting is inappropriate. We give an example. Assume that all responses are binary, Y t ∈ {0, 1}, t ≥ 1. Thus, the conditional expectation in (1.1) is based on binary observations (Y 1 , . . . , Y t , Y t+1 ) ∈ {0, 1} t+1 , and so is the ML model that is trained to approximate the forecast (1.1). However, the forecast Y t+1 ∈ [0, 1] imputed in (1.2) can take any value in the unit interval, e.g., Y t+1 = 0.46, and the forecast model (1.1) does not know how to deal with this input value, because it has never seen a value different from zero or one before (because it only learned to deal with binary inputs).
(2) A workaround of the problem discussed in item ( 1) is to learn a full simulation model from which one can simulate Y t+1 , given Y 1 , . . . , Y t . This then allows one to perform a Monte Carlo simulation extrapolation. This is the solution applied, e.g., in Wüthrich [21] and Delong et al. [6]. The main disadvantage of this approach clearly is that we need an accurate simulation model. If the responses Y t contain, e.g., claims payments, claims incurred and other stochastic processes, this is clearly beyond our modeling capabilities.
(3) The works of Kuo [9,10] present sequence-to-sequence forecasting methods, and the approach presented by Gabrielli [7] uses a rather similar technique. These approaches mask missing observations, and the predictive model learns to perform forecasting under incomplete information, e.g., it tries to directly predict Y t+2 , given (Y 1 , . . . , Y t ), by learning from all available information. This is a very suitable proposal. In practical applications, the main difficulty of this approach lies in controlling and mitigating potential biases during model training. Our proposal possesses thi
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