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.

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.

Évolution de la répartition de mise en charge au cours de la réadaptation chez les personnes présentant une hémiparésie consécutive à un accident vasculaire cérébral

Il est connu que les personnes ayant une hémiparésie à la suite d’un accident vasculaire cérébral (AVC) présentent une mise en charge (MEC) asymétrique lors de la station debout et lors du passage assis à debout (PAD). Par contre, peu d’études ont quantifié l’évolution de la MEC avec la réadaptation ou la précision avec laquelle ces personnes sont capables de la juger. L’objectif principal de ce projet était d’étudier l’évolution de la répartition et la perception de MEC en position debout et lors du PAD chez des personnes hémiparétiques en réadaptation fonctionnelle intensive (RFI). Un objectif secondaire était d’identifier les facteurs qui caractérisent les personnes hémiparétiques les plus asymétriques et les plus atteintes dans leur perception. Cette étude a été menée auprès de seize participants. Les résultats ont démontré qu’une asymétrie de répartition de l’appui en faveur du côté non parétique est présente dès les premiers mois après l’AVC et qu’elle persiste malgré la RFI. Chez les personnes avec une atteinte sévère de la fonction motrice, la MEC était plus symétrique pour le PAD que la station debout. En termes de perception, les personnes hémiparétiques étaient capables d’identifier le côté sur lequel ils mettaient plus d’appui mais ils avaient tendance à surestimer l’appui sur le côté parétique et donc à se juger moins asymétriques qu’ils ne l’étaient en réalité. Très peu de changements ont été observés lorsque les données au congé étaient comparées aux données à l’entrée dans l’étude. En réponse à l’objectif secondaire, la fonction motrice du membre inférieur parétique évaluée par le Chedoke et la différence de force des extenseurs entre les genoux étaient les facteurs les plus déterminants de l’asymétrie et de la perception de MEC. Les résultats obtenus constituent donc une étape supplémentaire vers la compréhension de la répartition asymétrique et les troubles de perception de MEC lors de la station debout et le PAD chez les personnes hémiparétiques. Il serait intéressant dans le futur d’explorer davantage les facteurs susceptibles d’influencer l’asymétrie et la perception de MEC et d’objectiver la relation de cause à effet entre ces deux variables en plus de préciser l’effet réel de l’asymétrie sur la stabilité posturale.

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.

Setilement of motor accidents claims with special reference to Kerala

The accident toll on our road traffic is staggering. Obviously this appalling toll of life and.health represents heavy economic loss in addition to human tragedy. the enormous increase in the number of motor vehicles with its rash, negligent and reckless use by unscrupulous, inexperienced and dangerous drivers in the most miserably managed roads coupled with concomitant hazards would draw our attention that Accident Prevention, and Accident compensation are thoroughly two compatiable aims. Proposed solutions to the traffic Problems abound. Preventive efforts concentrated on each of the variables the driver, the road and the vehicle are all being initiated. Still it is a Will the .Motor Vehicles are not considered as dangerous machines. Motoring activity is found useful.A competent and specially trained police force has to be created to deal with the traffic offences in a more scientific ways.The term ‘legal representative needs to be defined on the constructive aspects of relation and dependence.Services of legal aid and public counsels shall necessarily be extended to the poor Motor Accident victims.Timely reporting and timely investigation of Motor Accidents cases will reduce the number of fraudulent claims. There are instances where cases are taken in to investigation after several months of occurrence.It is hoped that the suggestions made above as a result of the present study, if pwgninto practice, may make a humble contribution to the prevention sssof motor accidents and to a faster and speedier settlement of motor accident compensation claims.

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.

Identifying job skills in commercial advisors in a health insurance company

The aim of this research was to identify the criticalcompetence of success of the commercial adviserin a company providing insurance and health services.For this research a sample of 34 commercialadvisers. The sample was divided into four groups(two per product and two per criterion of success).Systematic fi eld observations, interviews of criticalincidents, application of response tests and salesworkshops were used to evaluate the differentialcompetences that the successful advisers wereshowing in relation to the advisers de fi ned as average.The success criteria were based on the generatedcommission performance over the 10 months. Allin all, signi fi cant differences were found betweenthe “successful” and “average” groups. Furthermore,competences that correlate positively with atop sales performance were observed and competencesthat have major level of discrimination betweenthe “successful” and “average” groups wereestablished. Orientation to achievement, planningand management, information search, commercialaggressiveness and strategic vision are the competencesthat were considered to be key in the topperformance of a sales agent or commercial adviser.Additionally, the results in the response testswere analyzed in the four study groups, withoutobserving signi fi cant differences between them,which supports the theoretical framework of thepresent study.

Unemployment insurance : severance payments and informality in developing countries

We analyze whether the introduction or an increase of unemployment insurance (UI hereafter) beneÖts in developing countries reduces the e§ort made by unemployed workers to secure a new job in the formal sector. We adopt a comparative static approach and we consider the consequences of an increase of current UI beneÖts on unemployed workersídecision variables in this same period, i.e. we focus on an intra-temporal trade-o§, allowing us to assume away moral hazard complications. When there is no informal sector, unemployed workers may devote their time between e§ort to secure a new job in the formal sector and leisure. In the presence of an informal sector, unemployed workers may also devote time to remunerated informal activities. Consequently, the amount of e§ort devoted to secure a new (formal) job generates an opportunity cost, which ceteris paribus, reduces the amount of time devoted to remunerated activities in the informal sector. We show that in the presence of an informal sector, an increase of current UI beneÖts decreases this marginal opportunity cost and therefore unambiguously increases the e§ort undertaken to secure a new job in the formal sector. This intra-temporal e§ect is the only one at play in presence of one-shot UI beneÖts or with severance payments mechanism.

Unemployment insurance in the presence of an informal sector

We study the effect of UI benefits in a typical developing country where the informal sector is sizeable and persistent. In a partial equilibrium environment, ruling out the macroeconomic consequences of UI benefits, we characterize the stationary equilibrium of an economy where policyholders may be employed in the formal sector, short-run unemployed receiving UI benefits or long-run unemployed without UI benefits. We perform comparative static exercises to understand how UI benefits affect unemployed worker´s effort to secure a formal job, their labor supply in the informal sector and leisure time. Our model reveals that an increase in UI benefits generates two opposing effects for the short-run unemployed. First, since search efforts cannot be monitored it generates moral hazard behaviours that lower effort. Second, it generates an income effect as it reduces the marginal cost of searching for a formal job and increases effort.The overall effect is ambiguous and depends on the relative strength of these two effects. Additionally, we show that an increase in UI benefits increases the efforts of long-run unemployed workers. We provide a simple simulation exercise which suggests that the income effect pointed out is not necessarily of second-order importance in comparison with moral hazard strength. This result softens the widespread opinion, usually based on the microeconomic/partial equilibrium argument that the presence of dual labor markets is an obstacle to providing UI in developing countries.

Financial protection for the poor in Colombia: the effects of a subsidized health insurance scheme

Financial protection is one of the objectives of health systems, which protects poor households from falling into poverty as a result of health care related expenses. Expanding prepayment schemes to the poor is difficult in developing countries because labor is largely informal. Providing health care free-at-point-of-service does not adequately target spending on the poorest, but occupation- or community-based schemes have also inherent limitations to achieve universal coverage. Colombia adopted a government-subsidized health insurance scheme (SHI) strategy. The political debate about increasing SHI enrollment needs evidence about the effectiveness of this scheme regarding financial protection. This study runs a four-part model to estimate the effect of SHI on out-of-pocket expenses by the poor that are currently uninsured, if they were enrolled in the SHI. The results show a 43% and 50% reduction in expenses at Bogotá and national level respectively, which confirms the effectiveness of SHI as a financial protection tool.