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Author: Dameng Tang Publisher: ISBN: Category : Languages : en Pages :
Book Description
This thesis studies the applications of Pascal mixture models in three closely related topics in insurance and risk management. The first topic is on the modeling of correlated frequencies of operational risk (OR) losses from financial institutions. We propose a copula-free approach for modeling correlated frequencies using an Erlang-based multivariate mixed Poisson distribution. Many properties possessed by this class of distributions are investigated and a tailor-made generalized expectation-maximization (EM) algorithm is derived for fitting purposes. The applicability of the proposed distribution is illustrated in an OR management context, where this class is used to model the OR loss. The accuracy of the proposed approach is analyzed using a modified real operational loss data set. The second topic is about multivariate count regression with application in modeling correlated claim frequencies. We propose a multivariate Pascal mixture regression model as an alternative to understand the association between multivariate count response variables and their covariates. We examine the many properties possessed by this class of regression. A generalized EM algorithm is derived for fitting purposes, which also provides the standard errors of the regression coefficients which are useful for inference. Its applicability is demonstrated by fitting an automobile insurance claim count data set. The third topic is about modeling and predicting the number of incurred but not reported (IBNR) claims in Property Casualty (P) insurance. We model the claim arrival process together with the reporting delays as a marked Cox process whose intensity function is governed by a hidden Markov chain. The associated reported claim process and IBNR claim process remain to be marked Cox processes with easily convertible intensity functions and marking distributions. Closed-form expressions for both the autocorrelation function (ACF) and the distributions of the numbers of reported claims and IBNR claims are derived. A generalized EM algorithm is obtained to estimate the model parameters. The proposed model is examined through simulation studies and is also applied to a real insurance claim data set. We compare the predictive distributions of our model with those of the over-dispersed Poisson model (ODP), a stochastic model that underpins the widely used chain-ladder method.
Author: Dameng Tang Publisher: ISBN: Category : Languages : en Pages :
Book Description
This thesis studies the applications of Pascal mixture models in three closely related topics in insurance and risk management. The first topic is on the modeling of correlated frequencies of operational risk (OR) losses from financial institutions. We propose a copula-free approach for modeling correlated frequencies using an Erlang-based multivariate mixed Poisson distribution. Many properties possessed by this class of distributions are investigated and a tailor-made generalized expectation-maximization (EM) algorithm is derived for fitting purposes. The applicability of the proposed distribution is illustrated in an OR management context, where this class is used to model the OR loss. The accuracy of the proposed approach is analyzed using a modified real operational loss data set. The second topic is about multivariate count regression with application in modeling correlated claim frequencies. We propose a multivariate Pascal mixture regression model as an alternative to understand the association between multivariate count response variables and their covariates. We examine the many properties possessed by this class of regression. A generalized EM algorithm is derived for fitting purposes, which also provides the standard errors of the regression coefficients which are useful for inference. Its applicability is demonstrated by fitting an automobile insurance claim count data set. The third topic is about modeling and predicting the number of incurred but not reported (IBNR) claims in Property Casualty (P) insurance. We model the claim arrival process together with the reporting delays as a marked Cox process whose intensity function is governed by a hidden Markov chain. The associated reported claim process and IBNR claim process remain to be marked Cox processes with easily convertible intensity functions and marking distributions. Closed-form expressions for both the autocorrelation function (ACF) and the distributions of the numbers of reported claims and IBNR claims are derived. A generalized EM algorithm is obtained to estimate the model parameters. The proposed model is examined through simulation studies and is also applied to a real insurance claim data set. We compare the predictive distributions of our model with those of the over-dispersed Poisson model (ODP), a stochastic model that underpins the widely used chain-ladder method.
Author: Jacques Janssen Publisher: Springer Science & Business Media ISBN: 0387707301 Category : Mathematics Languages : en Pages : 441
Book Description
Everyone working in related fields from applied mathematicians to statisticians to actuaries and operations researchers will find this a brilliantly useful practical text. The book presents applications of semi-Markov processes in finance, insurance and reliability, using real-life problems as examples. After a presentation of the main probabilistic tools necessary for understanding of the book, the authors show how to apply semi-Markov processes in finance, starting from the axiomatic definition and continuing eventually to the most advanced financial tools.
Author: Liang Hong Publisher: ISBN: Category : Languages : en Pages : 13
Book Description
In the recent insurance literature, a variety of finite-dimensional parametric models have been proposed for analyzing the hump-shaped, heavy-tailed, and highly skewed loss data often encountered in applications. These parametric models are relatively simple, but they lack flexibility in the sense that an actuary analyzing a new data set cannot be sure that any one of these parametric models will be appropriate. As a consequence, the actuary must make a non-trivial choice among a collection of candidate models, putting him/herself at risk for various model misspecification biases. In this paper, we argue that, at least in cases where prediction of future insurance losses is the ultimate goal, there is reason to consider a single but more flexible nonparametric model. We focus here on Dirichlet process mixture models, and we reanalyze several of the standard insurance data sets to support our claim that model misspecification biases can be avoided by taking a nonparametric approach, with little to no cost, compared to existing parametric approaches.
Author: Daniela Anna Selch Publisher: Springer ISBN: 9783319928678 Category : Mathematics Languages : en Pages : 0
Book Description
This monograph presents a time-dynamic model for multivariate claim counts in actuarial applications. Inspired by real-world claim arrivals, the model balances interesting stylized facts (such as dependence across the components, over-dispersion and the clustering of claims) with a high level of mathematical tractability (including estimation, sampling and convergence results for large portfolios) and can thus be applied in various contexts (such as risk management and pricing of (re-)insurance contracts). The authors provide a detailed analysis of the proposed probabilistic model, discussing its relation to the existing literature, its statistical properties, different estimation strategies as well as possible applications and extensions. Actuaries and researchers working in risk management and premium pricing will find this book particularly interesting. Graduate-level probability theory, stochastic analysis and statistics are required.
Author: Edward W. Frees Publisher: ISBN: 9781139342681 Category : Actuarial science Languages : en Pages : 330
Book Description
Predictive modeling uses data to forecast future events. It exploits relationships between explanatory variables and the predicted variables from past occurrences to predict future outcomes. Forecasting financial events is a core skill that actuaries routinely apply in insurance and other risk-management applications. Predictive Modeling Applications in Actuarial Science emphasizes life-long learning by developing tools in an insurance context, providing the relevant actuarial applications, and introducing advanced statistical techniques that can be used to gain a competitive advantage in situations with complex data. Volume 2 examines applications of predictive modeling. Where Volume 1 developed the foundations of predictive modeling, Volume 2 explores practical uses for techniques, focusing on property and casualty insurance. Readers are exposed to a variety of techniques in concrete, real-life contexts that demonstrate their value and the overall value of predictive modeling, for seasoned practicing analysts as well as those just starting out.
Author: Marco Bee Publisher: ISBN: Category : Languages : en Pages : 27
Book Description
The purpose of this paper consists in analysing the relevance of dependence concepts in finance, insurance and risk management, exploring how these concepts can be implemented in a statistical model via copula functions and pointing out some difficulties related to this methodology. In particular, we first review the statistical models currently used in the actuarial and financial fields when dealing with loss data; then we show, by means of two risk management applications, that copula-based models are very flexible but sometimes difficult to set up and to estimate; finally we study, by means of a simulation experiment, the properties of the maximum likelihood estimators of the Gaussian and Gumbel copula.
Author: Frédéric Vrins Publisher: MDPI ISBN: 3039287605 Category : Business & Economics Languages : en Pages : 190
Book Description
Credit risk remains one of the major risks faced by most financial and credit institutions. It is deeply connected to the real economy due to the systemic nature of some banks, but also because well-managed lending facilities are key for wealth creation and technological innovation. This book is a collection of innovative papers in the field of credit risk management. Besides the probability of default (PD), the major driver of credit risk is the loss given default (LGD). In spite of its central importance, LGD modeling remains largely unexplored in the academic literature. This book proposes three contributions in the field. Ye & Bellotti exploit a large private dataset featuring non-performing loans to design a beta mixture model. Their model can be used to improve recovery rate forecasts and, therefore, to enhance capital requirement mechanisms. François uses instead the price of defaultable instruments to infer the determinants of market-implied recovery rates and finds that macroeconomic and long-term issuer specific factors are the main determinants of market-implied LGDs. Cheng & Cirillo address the problem of modeling the dependency between PD and LGD using an original, urn-based statistical model. Fadina & Schmidt propose an improvement of intensity-based default models by accounting for ambiguity around both the intensity process and the recovery rate. Another topic deserving more attention is trade credit, which consists of the supplier providing credit facilities to his customers. Whereas this is likely to stimulate exchanges in general, it also magnifies credit risk. This is a difficult problem that remains largely unexplored. Kanapickiene & Spicas propose a simple but yet practical model to assess trade credit risk associated with SMEs and microenterprises operating in Lithuania. Another topical area in credit risk is counterparty risk and all other adjustments (such as liquidity and capital adjustments), known as XVA. Chataignier & Crépey propose a genetic algorithm to compress CVA and to obtain affordable incremental figures. Anagnostou & Kandhai introduce a hidden Markov model to simulate exchange rate scenarios for counterparty risk. Eventually, Boursicot et al. analyzes CoCo bonds, and find that they reduce the total cost of debt, which is positive for shareholders. In a nutshell, all the featured papers contribute to shedding light on various aspects of credit risk management that have, so far, largely remained unexplored.
Author: Dameng Tang
Author: Dameng Tang
Author: Jacques Janssen
Author: Shuguang Zhang
Author: Liang Hong
Author: Daniela Anna Selch
Author: Edward W. Frees
Author: Marco Bee
Author: 
Author: 
Author: Frédéric Vrins