Some Applications of Markov Additive Processes as Models in Insurance and Financial Mathematics

Cette thèse est principalement constituée de trois articles traitant des processus markoviens additifs, des processus de Lévy et d'applications en finance et en assurance. Le premier chapitre est une introduction aux processus markoviens additifs (PMA), et une présentation du problème de ruine et de notions fondamentales des mathématiques financières. Le deuxième chapitre est essentiellement l'article "Lévy Systems and the Time Value of Ruin for Markov Additive Processes" écrit en collaboration avec Manuel Morales et publié dans la revue European Actuarial Journal. Cet article étudie le problème de ruine pour un processus de risque markovien additif. Une identification de systèmes de Lévy est obtenue et utilisée pour donner une expression de l'espérance de la fonction de pénalité actualisée lorsque le PMA est un processus de Lévy avec changement de régimes. Celle-ci est une généralisation des résultats existant dans la littérature pour les processus de risque de Lévy et les processus de risque markoviens additifs avec sauts "phase-type". Le troisième chapitre contient l'article "On a Generalization of the Expected Discounted Penalty Function to Include Deficits at and Beyond Ruin" qui est soumis pour publication. Cet article présente une extension de l'espérance de la fonction de pénalité actualisée pour un processus subordinateur de risque perturbé par un mouvement brownien. Cette extension contient une série de fonctions escomptée éspérée des minima successives dus aux sauts du processus de risque après la ruine. Celle-ci a des applications importantes en gestion de risque et est utilisée pour déterminer la valeur espérée du capital d'injection actualisé. Finallement, le quatrième chapitre contient l'article "The Minimal entropy martingale measure (MEMM) for a Markov-modulated exponential Lévy model" écrit en collaboration avec Romuald Hervé Momeya et publié dans la revue Asia-Pacific Financial Market. Cet article présente de nouveaux résultats en lien avec le problème de l'incomplétude dans un marché financier où le processus de prix de l'actif risqué est décrit par un modèle exponentiel markovien additif. Ces résultats consistent à charactériser la mesure martingale satisfaisant le critère de l'entropie. Cette mesure est utilisée pour calculer le prix d'une option, ainsi que des portefeuilles de couverture dans un modèle exponentiel de Lévy avec changement de régimes.

Les coûts des soins de santé chez les personnes âgées de 65 ans et plus avec incapacités au Québec

La question des coûts des soins de santé gagne en intérêt dans le contexte du vieillissement de la population. On sait que les personnes en moins bonne santé, bien que vivant moins longtemps, sont associées à des coûts plus élevés. On s'intéresse aux facteurs associés à des coûts publics des soins de santé plus élevés au niveau individuel, chez les Québécois vivant en ménage privé âgés de 65 ans et plus, présentant au moins un type d’incapacité. À l’aide de modèles de régression, la variation des coûts pour la consultation de professionnels de la santé et la prise de médicaments a été analysée en fonction du nombre d’incapacités ainsi que de la nature de celles-ci. Les informations sur l’état de santé et la situation socio-démographique proviennent de l’Enquête sur les limitations d’activités (EQLA) de 1998, celles sur les coûts du Fichier d’inscription des personnes assurées (FIPA) de la Régie de l’Assurance maladie du Québec (RAMQ), pour la même année. Les résultats montrent que les deux types de coûts considérés augmentent en fonction du nombre d’incapacités. D’autre part, des coûts plus élevés ont été trouvés chez les personnes présentant une incapacité liée à l’agilité concernant la consultation de professionnels de la santé, alors que, concernant la prise de médicaments, le même constat s’applique aux personnes avec une incapacité liée à la mobilité. Les deux types de coûts considérés présentent un niveau plus élevé chez les personnes présentant une incapacité liée au psychisme, en particulier lorsque l’on considère la prise de médicaments. Ces observations soulignent l’intérêt de considérer la nature du problème de santé lorsque l’on étudie les déterminants individuels du niveau des coûts des soins de santé.

On the design of customized risk measures in insurance, the problem of capital allocation and the theory of fluctuations for Lévy processes

Dans cette thèse, nous étudions quelques problèmes fondamentaux en mathématiques financières et actuarielles, ainsi que leurs applications. Cette thèse est constituée de trois contributions portant principalement sur la théorie de la mesure de risques, le problème de l’allocation du capital et la théorie des fluctuations. Dans le chapitre 2, nous construisons de nouvelles mesures de risque cohérentes et étudions l’allocation de capital dans le cadre de la théorie des risques collectifs. Pour ce faire, nous introduisons la famille des "mesures de risque entropique cumulatifs" (Cumulative Entropic Risk Measures). Le chapitre 3 étudie le problème du portefeuille optimal pour le Entropic Value at Risk dans le cas où les rendements sont modélisés par un processus de diffusion à sauts (Jump-Diffusion). Dans le chapitre 4, nous généralisons la notion de "statistiques naturelles de risque" (natural risk statistics) au cadre multivarié. Cette extension non-triviale produit des mesures de risque multivariées construites à partir des données financiéres et de données d’assurance. Le chapitre 5 introduit les concepts de "drawdown" et de la "vitesse d’épuisement" (speed of depletion) dans la théorie de la ruine. Nous étudions ces concepts pour des modeles de risque décrits par une famille de processus de Lévy spectrallement négatifs.

Disability is in the Eye of the Beholder

Travail créatif / Creative Work

When Disability Rhymes with Negative Bias: A Response to Verpaelst

Commentaire / Commentary

Ambiguity on the insurer's side: the demand for insurance

Empirical evidence suggests that ambiguity is prevalent in insurance pricing and underwriting, and that often insurers tend to exhibit more ambiguity than the insured individuals (e.g., [23]). Motivated by these findings, we consider a problem of demand for insurance indemnity schedules, where the insurer has ambiguous beliefs about the realizations of the insurable loss, whereas the insured is an expected-utility maximizer. We show that if the ambiguous beliefs of the insurer satisfy a property of compatibility with the non-ambiguous beliefs of the insured, then there exist optimal monotonic indemnity schedules. By virtue of monotonicity, no ex-post moral hazard issues arise at our solutions (e.g., [25]). In addition, in the case where the insurer is either ambiguity-seeking or ambiguity-averse, we show that the problem of determining the optimal indemnity schedule reduces to that of solving an auxiliary problem that is simpler than the original one in that it does not involve ambiguity. Finally, under additional assumptions, we give an explicit characterization of the optimal indemnity schedule for the insured, and we show how our results naturally extend the classical result of Arrow [5] on the optimality of the deductible indemnity schedule.

Ambiguity on the insurer's side: the demand for insurance

Empirical evidence suggests that ambiguity is prevalent in insurance pricing and underwriting, and that often insurers tend to exhibit more ambiguity than the insured individuals (e.g., [23]). Motivated by these findings, we consider a problem of demand for insurance indemnity schedules, where the insurer has ambiguous beliefs about the realizations of the insurable loss, whereas the insured is an expected-utility maximizer. We show that if the ambiguous beliefs of the insurer satisfy a property of compatibility with the non-ambiguous beliefs of the insured, then there exist optimal monotonic indemnity schedules. By virtue of monotonicity, no ex-post moral hazard issues arise at our solutions (e.g., [25]). In addition, in the case where the insurer is either ambiguity-seeking or ambiguity-averse, we show that the problem of determining the optimal indemnity schedule reduces to that of solving an auxiliary problem that is simpler than the original one in that it does not involve ambiguity. Finally, under additional assumptions, we give an explicit characterization of the optimal indemnity schedule for the insured, and we show how our results naturally extend the classical result of Arrow [5] on the optimality of the deductible indemnity schedule.

The Financial Statement Insurance Alternative to Auditor Liability

These articles evaluate using financial statement insurance (FSI) to reduce the frequency and magnitude of audit failure. The FSI concept was pioneered by Josh Ronen, NYU Accounting Professor, who has modeled its economic aspects. My paper examines FSI’s efficacy from policy and legal perspectives. I conclude that while the model is not perfect, it promises considerable advantages over the current model. While some of the existing system’s imperfections are sustained or reappear in different guises, none of the existing imperfections appears to be aggravated and the rest likely are mitigated significantly. So I prescribe a framework to permit companies, on an experimental-basis and with investor approval, to use FSI as an optional alternative to financial statement auditing backed by auditor liability.

Rashtriya Swasthya Bhima Yojana-Comprehensive Health Insurance Scheme (Rsby-Chis) In Kerala: A Study On The Effectiveness And Utilization Of The Scheme With Special Reference To Ernakulam And Wayanad Districts

Health insurance has become a necessity for the common man, next to food, clothing and shelter. The financing of health expense is either catastrophic or sometimes even frequently contracted illnesses, is a major cause of mental agony for the common man. The cost of care may sometimes result in the complete erosion of the family savings or may even lead to indebtedness as many studies on causes of rural indebtedness bear testimony (Jayalakshmi, 2006). A suitable cover by way of health insurance is all that is required to cope with such situations. Health care insurance rightly provides the mechanism for both individuals and families to mitigate the financial burden of medical expenses in the present context. Hence a well designed affordable health insurance policy is the need of the hour.Therefore, it is very significant to study the extent to which the beneficiaries in Kerala make use of the benefits provided by a social health insurance scheme like RSBY-CHIS. Based on the above pertinent points, this study assumes national relevance even though the geographical area of the study is limited to two districts of Kerala. The findings of the study will bring forth valuable inputs on the services availed by the beneficiaries of RSBYCHIS and take appropriate measures to improve the effectiveness of the scheme whereby maximum quality benefit could be availed by the poorest of the poor and develop the scheme as a real dawn of the new era of health for them

Determinants of Consumer Purchase Decisions of Health Insurance in Kerala

This research work was to study the level of awareness of consumers about health insurance concept and market, consumer perceptions about health insurance providers, schemes and various factors that influence buying decision of health insurance. There is need to bring entire age group – high risk and low risk under health insurance cover. Widening the cover of health insurance calls for indepth understanding of consumer thinking and extensive marketing efforts based on that. Hence the study of consumer perceptions and the impact of different contributing factors on consumer purchase decision assume significance to the marketer. Understanding the consumer thinking on health insurance will also be of relevance to governmental/non governmental agencies, as affordable health care to all is a policy objective of the government and new schemes are being launched in this area.

Learning disability prediction tool using ANN and ANFIS

Learning Disability (LD) is a neurological condition that affects a child’s brain and impairs his ability to carry out one or many specific tasks. LD affects about 15 % of children enrolled in schools. The prediction of LD is a vital and intricate job. The aim of this paper is to design an effective and powerful tool, using the two intelligent methods viz., Artificial Neural Network and Adaptive Neuro-Fuzzy Inference System, for measuring the percentage of LD that affected in school-age children. In this study, we are proposing some soft computing methods in data preprocessing for improving the accuracy of the tool as well as the classifier. The data preprocessing is performed through Principal Component Analysis for attribute reduction and closest fit algorithm is used for imputing missing values. The main idea in developing the LD prediction tool is not only to predict the LD present in children but also to measure its percentage along with its class like low or minor or major. The system is implemented in Mathworks Software MatLab 7.10. The results obtained from this study have illustrated that the designed prediction system or tool is capable of measuring the LD effectively

Testing for Hidden Information and Action in Automobile Insurance Market

I test the presence of hidden information and action in the automobile insurance market using a data set from several Colombian insurers. To identify the presence of hidden information I find a common knowledge variable providing information on policyholder s risk type which is related to both experienced risk and insurance demand and that was excluded from the pricing mechanism. Such unused variable is the record of policyholder s traffic offenses. I find evidence of adverse selection in six of the nine insurance companies for which the test is performed. From the point of view of hidden action I develop a dynamic model of effort in accident prevention given an insurance contract with bonus experience rating scheme and I show that individual accident probability decreases with previous accidents. This result brings a testable implication for the empirical identification of hidden action and based on that result I estimate an econometric model of the time spans between the purchase of the insurance and the first claim, between the first claim and the second one, and so on. I find strong evidence on the existence of unobserved heterogeneity that deceives the testable implication. Once the unobserved heterogeneity is controlled, I find conclusive statistical grounds supporting the presence of moral hazard in the Colombian insurance market.

Disability as a determinant of access to health care services in Colombia

The relationship between disability and poverty has been described in different contexts. Nevertheless, the basic characteristics of this relationship have not yet been fully established. The social exclusion and discrimination against people with disabilities increase the risk of poverty and reduce the access to basic opportunities such as health and education. This study examines the impact of a health limitation and poverty in the access to health care services in Colombia. Data from the Colombian National Health Survey (2007) was used in the analysis. Variables related with health condition and socio economic characteristics were first generated. Then interactions between health limitations and the lower levels of the asset index were created. This variable gave information related to the relationship between disability and poverty. A probabilistic model was estimated to examine the impact of a health condition and the relation between poverty and disability on the access to health care. The results suggest that living with a physical limitation increases by 10% the probability of access to health care services in Colombia. However, people with a disability and in the lowest quartile of the asset index have a 5% less probability of access to health care services. We conclude that people who live with a physical, mental or sensorial limitation have a higher probability of access to health care services. However, poor and disabled people have a lower probability in access, which increases the risk of having a severe disease and become chronically poor.