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Micro-Level Stochastic Loss Reserving for General Insurance

Author : Katrien Antonio

Publisher :

Page : 24 pages

File Size : 33,68 MB

Release : 2017

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ISBN :

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Book Description

To meet future liabilities general insurance companies will set-up reserves. Predicting future cash-flows is essential in this process. Actuarial loss reserving methods will help them to do this in a sound way. The last decennium a vast literature about stochastic loss reserving for the general insurance business has been developed. Apart from few exceptions, all of these papers are based on data aggregated in run-off triangles. However, such an aggregate data set is a summary of an underlying, much more detailed data base that is available to the insurance company. We refer to this data set at individual claim level as "micro-level data." We investigate whether the use of such micro-level claim data can improve the reserving process. A realistic micro-level data set on liability claims (material and injury) from a European insurance company is modeled. Stochastic processes are specified for the various aspects involved in the development of a claim: the time of occurrence, the delay between occurrence and the time of reporting to the company, the occurrence of payments and their size and the final settlement of the claim. These processes are calibrated to the historical individual data of the portfolio and used for the projection of future claims. Through an out-of-sample prediction exercise we show that the micro-level approach provides the actuary with detailed and valuable reserve calculations. A comparison with results from traditional actuarial reserving techniques is included. For our case-study reserve calculations based on the micro-level model are to be preferred; compared to traditional methods, they reflect real outcomes in a more realistic way.



Micro-level Stochastic Loss Reserving Models for Insurance

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Publisher :

Page : 161 pages

File Size : 46,39 MB

Release : 2014

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Book Description

Accurate loss reserves are essential for insurers to maintain adequate capital and to efficiently price their insurance products. Loss reserving for Property & Casualty insurance is usually based on macro-level models with aggregate data in a run-off triangle. The macro-level models may generate material errors in the reserve estimates when assumptions underlying the estimates evolve over time in an unanticipated way. In recent years, a small set of literature has proposed reserving models that use underlying individual claims data to estimate outstanding liabilities based on individual claim level information, analogous to approaches used in the life insurance industry. These models are referred to as "micro-level models". In this dissertation, I specify a micro-level model with a hierarchical structure to model the individual claim development that has the flexibility to accommodate assumptions that evolve dynamically over time. The dissertation consists of a simulation study and an empirical study. In the simulation study, I simulate claims data under different environmental changes and use both the macro- and micro-level models to estimate the outstanding liabilities. The results demonstrate that there are many scenarios in which the micro-level model outperforms the macro-level model by generating reserve estimates with smaller reserve errors and higher precision. For actuaries responsible for setting reserves, this study highlights scenarios in which micro-level models outperform traditional macro-level models and so can provide a new tool to provide insights when establishing accurate loss reserves. In the empirical study, I demonstrate the application of a micro-level model in a large portfolio of workers compensation insurance provided by a major P&C insurer. The model is estimated with historic data, validated with a hold-out sample, and compared with commonly-used macro-level models. I show that the micro-level model provides a more realistic reserve estimate than that given by the macro-level models, and the estimation error is largely reduced through the use of individual claims data. The micro-level model is more likely to capture the downside potential in reserves and to provide adequate allowance when extreme scenarios occur. I conclude that micro-level models provide valuable alternatives to traditional models for loss reserving.



Stochastic Loss Reserving Using Generalized Linear Models

Author : Greg Taylor

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Page : 100 pages

File Size : 10,24 MB

Release : 2016-05-04

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ISBN : 9780996889704

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Book Description

In this monograph, authors Greg Taylor and Gráinne McGuire discuss generalized linear models (GLM) for loss reserving, beginning with strong emphasis on the chain ladder. The chain ladder is formulated in a GLM context, as is the statistical distribution of the loss reserve. This structure is then used to test the need for departure from the chain ladder model and to consider natural extensions of the chain ladder model that lend themselves to the GLM framework.



Claims Reserving in General Insurance

Author : David Hindley

Publisher : Cambridge University Press

Page : 514 pages

File Size : 20,78 MB

Release : 2017-10-26

Category : Mathematics

ISBN : 1108514847

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Book Description

This is a comprehensive and accessible reference source that documents the theoretical and practical aspects of all the key deterministic and stochastic reserving methods that have been developed for use in general insurance. Worked examples and mathematical details are included, along with many of the broader topics associated with reserving in practice. The key features of reserving in a range of different contexts in the UK and elsewhere are also covered. The book contains material that will appeal to anyone with an interest in claims reserving. It can be used as a learning resource for actuarial students who are studying the relevant parts of their professional bodies' examinations, as well as by others who are new to the subject. More experienced insurance and other professionals can use the book to refresh or expand their knowledge in any of the wide range of reserving topics covered in the book.



Stochastic Claims Reserving Methods in Insurance

Author : Mario V. Wüthrich

Publisher : John Wiley & Sons

Page : 438 pages

File Size : 10,77 MB

Release : 2008-04-30

Category : Business & Economics

ISBN : 0470772727

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Book Description

Claims reserving is central to the insurance industry. Insurance liabilities depend on a number of different risk factors which need to be predicted accurately. This prediction of risk factors and outstanding loss liabilities is the core for pricing insurance products, determining the profitability of an insurance company and for considering the financial strength (solvency) of the company. Following several high-profile company insolvencies, regulatory requirements have moved towards a risk-adjusted basis which has lead to the Solvency II developments. The key focus in the new regime is that financial companies need to analyze adverse developments in their portfolios. Reserving actuaries now have to not only estimate reserves for the outstanding loss liabilities but also to quantify possible shortfalls in these reserves that may lead to potential losses. Such an analysis requires stochastic modeling of loss liability cash flows and it can only be done within a stochastic framework. Therefore stochastic loss liability modeling and quantifying prediction uncertainties has become standard under the new legal framework for the financial industry. This book covers all the mathematical theory and practical guidance needed in order to adhere to these stochastic techniques. Starting with the basic mathematical methods, working right through to the latest developments relevant for practical applications; readers will find out how to estimate total claims reserves while at the same time predicting errors and uncertainty are quantified. Accompanying datasets demonstrate all the techniques, which are easily implemented in a spreadsheet. A practical and essential guide, this book is a must-read in the light of the new solvency requirements for the whole insurance industry.





Loss Reserving

Author : Gregory Taylor

Publisher : Springer Science & Business Media

Page : 396 pages

File Size : 35,91 MB

Release : 2012-12-06

Category : Business & Economics

ISBN : 1461545838

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Book Description

All property and casualty insurers are required to carry out loss reserving as a statutory accounting function. Thus, loss reserving is an essential sphere of activity, and one with its own specialized body of knowledge. While few books have been devoted to the topic, the amount of published research literature on loss reserving has almost doubled in size during the last fifteen years. Greg Taylor's book aims to provide a comprehensive, state-of-the-art treatment of loss reserving that reflects contemporary research advances to date. Divided into two parts, the book covers both the conventional techniques widely used in practice, and more specialized loss reserving techniques employing stochastic models. Part I, Deterministic Models, covers very practical issues through the abundant use of numerical examples that fully develop the techniques under consideration. Part II, Stochastic Models, begins with a chapter that sets up the additional theoretical material needed to illustrate stochastic modeling. The remaining chapters in Part II are self-contained, and thus can be approached independently of each other. A special feature of the book is the use throughout of a single real life data set to illustrate the numerical examples and new techniques presented. The data set illustrates most of the difficult situations presented in actuarial practice. This book will meet the needs for a reference work as well as for a textbook on loss reserving.



A Multi-State Approach and Flexible Payment Distributions for Micro-Level Reserving in General Insurance

Author : Katrien Antonio

Publisher :

Page : 35 pages

File Size : 48,74 MB

Release : 2016

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ISBN :

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Book Description

Insurance companies hold reserves to be able to fulfill future liabilities with respect to the policies they write. Micro-level reserving methods focus on the development of individual claims over time, providing an alternative to the classical techniques that aggregate the development of claims into run-off triangles. This paper presents a discrete-time multi-state framework that reconstructs the claim development process as a series of transitions between a given set of states. The states in our setting represent the events that may happen over the lifetime of a claim, i.e. reporting, intermediate payments and closure. For each intermediate payment we model the payment distribution separately. To this end, we use a body-tail approach where the body of the distribution is modeled separately from the tail. Generalized Additive Models for Location, Scale and Shape introduced by Stasinopoulos and Rigby (2007) allow for flexible modeling of the body distribution while incorporating co-variate information. We use the toolbox from Extreme Value Theory to determine the threshold separating the body from the tail and to model the tail of the payment distributions. We do not correct payments for inflation beforehand, but include relevant co-variate information in the model. Using these building blocks, we outline a simulation procedure to evaluate the RBNS reserve. The method is applied to a real life data set, and we benchmark our results by means of a back test.



Handbook on Loss Reserving

Author : Michael Radtke

Publisher : Springer

Page : 317 pages

File Size : 32,35 MB

Release : 2016-10-26

Category : Business & Economics

ISBN : 3319300563

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Book Description

This handbook presents the basic aspects of actuarial loss reserving. Besides the traditional methods, it also includes a description of more recent ones and a discussion of certain problems occurring in actuarial practice, like inflation, scarce data, large claims, slow loss development, the use of market statistics, the need for simulation techniques and the task of calculating best estimates and ranges of future losses. In property and casualty insurance the provisions for payment obligations from losses that have occurred but have not yet been settled usually constitute the largest item on the liabilities side of an insurer's balance sheet. For this reason, the determination and evaluation of these loss reserves is of considerable economic importance for every property and casualty insurer. Actuarial students, academics as well as practicing actuaries will benefit from this overview of the most important actuarial methods of loss reserving by developing an understanding of the underlying stochastic models and how to practically solve some problems which may occur in actuarial practice.



A Multivariate Micro-Level Insurance Counts Model With a Cox Process Approach

Author : Benjamin Avanzi

Publisher :

Page : 24 pages

File Size : 13,79 MB

Release : 2019

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Book Description

When calculating the risk margins of a company with multiple Lines of Business-typically, a quantile in the right tail of an aggregate loss, assumptions about the dependence structure between the different Lines are crucial. Many current multivariate reserving methodologies focus on aggregated claims information, typically in the format of claim triangles. This aggregation is subject to some inefficiencies, such as possibly insufficient data points, and potential elimination of useful information. This inefficiency is particularly problematic for the estimation of dependence. So-called 'micro-level models', on the other hand, utilise more granular levels of observations. Such granular data lend themselves naturally to a stochastic process modelling approach. However, the literature interested in the incorporation of a dependency structure with a micro-level approach is still scarce.In this paper, we extend the literature of micro-level stochastic reserving models to the multivariate context. We develop a multivariate Cox process to model the joint arrival process of insurance claims in multiple Lines of Business. This allows for a dependency structure between the frequencies of claims. We also explicitly incorporate known covariates, such as seasonality patterns and trends, which may explain some of the relationship between two insurance processes (or at least help tease out those relationships). We develop a filtering algorithm to estimate the unobservable stochastic intensities. Model calibration is illustrated using real data from the AUSI data set.