85 research outputs found
Heavy-tailed distribution in the presence of dependence in insurance and finance
In the past decade, the study of the renewal risk model in the presence of dependent insurance and financial risks and heavy-tailed claims is one of the key topics in modern risk theory. The purpose of this thesis is to study the renewal risk model with certain dependence structures. We also assume that claim sizes follow a heavy-tailed distribution, in particular, a subexponential distribution. We focus on studying the impact of heavy tails and dependence structures on ruin probabilities and the tail probabilities of aggregate claims. For the study of dependence structure, we consider two assumptions here, namely, dependence between claims and inter-arrival times and dependence between insurance and financial risks, particular attention are paid for the dependent insurance and financial risks. In this case, an equation for the tail probability of maximal present value of aggregate net loss is derived, and hence some insights into the ruin probability can be obtained
Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields
This book covers a broad range of research results in the field of Markov and Semi-Markov chains, processes, systems and related emerging fields. The authors of the included research papers are well-known researchers in their field. The book presents the state-of-the-art and ideas for further research for theorists in the fields. Nonetheless, it also provides straightforwardly applicable results for diverse areas of practitioners
Current Topics on Risk Analysis: ICRA6 and RISK2015 Conference
Peer ReviewedPostprint (published version
Current Topics on Risk Analysis: ICRA6 and RISK2015 Conference
Artículos presentados en la International Conference on Risk Analysis ICRA 6/RISK
2015, celebrada en Barcelona del 26 al 29 de mayo de 2015.Peer ReviewedPostprint (published version
Pairwise versus mutual independence: visualisation, actuarial applications and central limit theorems
Accurately capturing the dependence between risks, if it exists, is an increasingly relevant topic of actuarial research. In recent years, several authors have started to relax the traditional 'independence assumption', in a variety of actuarial settings. While it is known that 'mutual independence' between random variables is not equivalent to their 'pairwise independence', this thesis aims to provide a better understanding of the materiality of this difference. The distinction between mutual and pairwise independence matters because, in practice, dependence is often assessed via pairs only, e.g., through correlation matrices, rank-based measures of association, scatterplot matrices, heat-maps, etc. Using such pairwise methods, it is possible to miss some forms of dependence. In this thesis, we explore how material the difference between pairwise and mutual independence is, and from several angles.
We provide relevant background and motivation for this thesis in Chapter 1, then conduct a literature review in Chapter 2.
In Chapter 3, we focus on visualising the difference between pairwise and mutual independence. To do so, we propose a series of theoretical examples (some of them new) where random variables are pairwise independent but (mutually) dependent, in short, PIBD. We then develop new visualisation tools and use them to illustrate what PIBD variables can look like. We showcase that the dependence involved is possibly very strong. We also use our visualisation tools to identify subtle forms of dependence, which would otherwise be hard to detect.
In Chapter 4, we review common dependence models (such has elliptical distributions and Archimedean copulas) used in actuarial science and show that they do not allow for the possibility of PIBD data. We also investigate concrete consequences of the 'nonequivalence' between pairwise and mutual independence. We establish that many results which hold for mutually independent variables do not hold under sole pairwise independent. Those include results about finite sums of random variables, extreme value theory and bootstrap methods. This part thus illustrates what can potentially 'go wrong' if one assumes mutual independence where only pairwise independence holds.
Lastly, in Chapters 5 and 6, we investigate the question of what happens for PIBD variables 'in the limit', i.e., when the sample size goes to infi nity. We want to see if the 'problems' caused by dependence vanish for sufficiently large samples. This is a broad question, and we concentrate on the important classical Central Limit Theorem (CLT), for which we fi nd that the answer is largely negative. In particular, we construct new sequences of PIBD variables (with arbitrary margins) for which a CLT does not hold. We derive explicitly the asymptotic distribution of the standardised mean of our sequences, which allows us to illustrate the extent of the 'failure' of a CLT for PIBD variables. We also propose a general methodology to construct dependent K-tuplewise independent (K an arbitrary integer) sequences of random variables with arbitrary margins. In the case K = 3, we use this methodology to derive explicit examples of triplewise independent sequences for which no CLT hold. Those results illustrate that mutual independence is a crucial assumption within CLTs, and that having larger samples is not always a viable solution to the problem of non-independent data
Sistemas de alarme ótimos e sua aplicação a séries financeiras
Doutoramento em MatemáticaThis thesis focuses on the application of optimal alarm systems to non linear
time series models. The most common classes of models in the analysis of
real-valued and integer-valued time series are described. The construction
of optimal alarm systems is covered and its applications explored.
Considering models with conditional heteroscedasticity, particular attention
is given to the Fractionally Integrated Asymmetric Power ARCH,
FIAPARCH(p; d; q) model and an optimal alarm system is implemented, following
both classical and Bayesian methodologies.
Taking into consideration the particular characteristics of the APARCH(p; q)
representation for financial time series, the introduction of a possible counterpart
for modelling time series of counts is proposed: the INteger-valued
Asymmetric Power ARCH, INAPARCH(p; q). The probabilistic properties
of the INAPARCH(1; 1) model are comprehensively studied, the conditional
maximum likelihood (ML) estimation method is applied and the asymptotic
properties of the conditional ML estimator are obtained. The final part of
the work consists on the implementation of an optimal alarm system to the
INAPARCH(1; 1) model. An application is presented to real data series.Esta tese centra-se na aplicação de sistemas de alarme ótimos a modelos
de séries temporais não lineares. As classes de modelos mais comuns na
análise de séries temporais de valores reais e de valores inteiros são descritas
com alguma profundidade. É abordada a construção de sistemas de alarme
ótimos e as suas aplicações são exploradas.
De entre os modelos com heterocedasticidade condicional é dada especial
atenção ao modelo ARCH Fraccionalmente Integrável de Potência Assimétrica,
FIAPARCH(p; d; q), e é feita a implementação de um sistema de
alarme ótimo, considerando ambas as metodologias clássica e Bayesiana.
Tomando em consideração as características particulares do modelo
APARCH(p; q) na aplicação a séries de dados financeiros, é proposta
a introdução do seu homólogo para a modelação de séries temporais
de contagens: o modelo ARCH de valores INteiros e Potência Assimétrica,
INAPARCH(p; q). As propriedades probabilísticas do modelo
INAPARCH(1; 1) são extensivamente estudadas, é aplicado o método da
máxima verosimilhança (MV) condicional para a estimação dos parâmetros
do modelo e estudadas as propriedades assintóticas do estimador de MV
condicional. Na parte final do trabalho é feita a implementação de um
sistema de alarme ótimo ao modelo INAPARCH(1; 1) e apresenta-se uma
aplicação a séries de dados reais
Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain
The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio
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