On the Expected Discounted Penalty Function for the Classical Risk Model with Potentially Delayed Claims and Random Incomes

We focus on the expected discounted penalty function of a compound Poisson risk model with random incomes and potentially delayed claims. It is assumed that each main claim will produce a byclaim with a certain probability and the occurrence of the byclaim may be delayed depending on associated main claim amount. In addition, the premium number process is assumed as a Poisson process. We derive the integral equation satisfied by the expected discounted penalty function. Given that the premium size is exponentially distributed, the explicit expression for the Laplace transform of the expected discounted penalty function is derived. Finally, for the exponential claim sizes, we present the explicit formula for the expected discounted penalty function

On modeling quantities for insurer solvency against catastrophe under some Markovian assumptions

Insurance companies sometimes face catastrophic losses, yet they must remain solvent enough to meet the legal obligation of covering all claims. Catastrophes can result in large damages to the policyholders, causing the arrival of numerous claims to insurance companies at once. Furthermore, the severity of an event could impact the time until the next occurrence. An insurer needs certain levels of startup capital to meet all claims, and then must have adequate reserves on a continual basis, even more so when catastrophes occur. This work examines two facets of these matters: for an infinite time horizon, we extend and develop models for insurer bankruptcy-related quantities accounting for the reality of large claims occurring. Meanwhile, for finite time horizons, we model the present value of claims that have been incurred but not yet reported, so-called \u27IBNR\u27 claims. In the former, we show how our method for \u27Gerber-Shiu\u27 functions works in a recently proposed dependency structure allowing insurers to charge clients different premiums depending on their riskiness. In the latter, we build upon a recent method which allowed claims to arrive in batches; besides permitting discounting to be time-dependent, we allow the insurer to adjust the assumed distribution of the time until the next event by comparing the number of claims from the current event to any number of random intervals. We provide numerical studies for both scenarios --Abstract, page iii

Risk Pooling in Health Care Financing: The Implications for Health System Performance

Pooling is the health system function whereby collected health revenues are transferred to purchasing organizations. Pooling ensures that the risk related to financing health interventions is borne by all the members of the pool and not by each contributor individually. Its main purpose is to share the financial risk associated with health interventions for which there is uncertain need. The arguments in favor of risk pooling in health care embody equity and efficiency considerations. The equity arguments reflect the view that society does not consider it to be fair that individuals should assume all the risk associated with their health care expenditure needs. The efficiency arguments arise because pooling can lead to major improvements in population health, can increase productivity, and reduces uncertainty associated with health care expenditure. The report considers four classes of risk pooling: no risk pool, under which all expenditure liability lies with the individual; unitary risk pool, under which all expenditure liability is transferred to a single national pool; fragmented risk pools, under which a series of independent risk pools (such as local governments or employer-based pools) are used; and integrated risk pools, under which fragmented risk pools are compensated for the variations in risk to which they are exposed. It notes that small, fragmented risk pools, which are the norm in developing countries, contribute to seriously adverse outcomes for health system performance. It therefore argues strongly for integration of risk pools as an important health system stewardship responsibility. There are numerous practical difficulties in making integration operational, so the report offers some guidance on implementation, noting that optimal design of risk pooling arrangements depends heavily on local circumstances. It concludes with suggestions for a number of measures of health system performance that can offer indications of the success of risk pool integration.sch_iihpub3377pu

Asset Pricing with Revealed Utility.

This dissertation consists of two essays that interpret crime as revealed marginal utility of heterogeneous consumers, and investigates its implications for asset pricing. The first chapter proposes crime as a revealed response of individuals that derive utility from relative wealth. Using daily reported crime incidents from over 2,500 law enforcement agencies across 27 states from 1991-2012, a contemporaneous relationship between daily stock returns and various types of crimes are found. Market changes also impact investors’ and non-investors’ utility differently and this is interpreted as evidence in support of envy models such as Abel (1990) that individuals care about their own wealth relative to others. For example, daily stock market increases are associated with decreases in violent crimes in high income locations, while market increases are associated with increases in violent crime in low income locations. The second chapter builds upon using crime as revealed marginal utility. Having established a relationship between violent crime and the stock market in the first chapter, the second chapter proposes violent crime growth as a measure of revealed marginal utility growth of heterogeneous consumers in incomplete markets to price the cross-section of stock returns. Consumer heterogeneity is measured using the cross-sectional average and cross-sectional variance of crime growth exploiting a monthly panel of reported crime incidents from over 10,000 law enforcement agencies across the United States from 1975-2012. Consistent with heterogeneous consumer models such as Mankiw (1986), the cross-sectional average and variance of violent crime growth are found to explain the cross-section of stock returns. Specifically, investors pay a premium for assets that have higher betas to the violent crime growth moments.PhDBusiness AdministrationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133289/1/jrhuck_1.pd

Aligning capital with risk

The interaction of capital and risk is of primary interest in the corporate governance of banks as it links operational profitability and strategic risk management. Senior executives understand that their organization's monitoring system strongly affects the behaviour of managers and employees. Typical instruments used by senior executives to focus on strategy are balanced scorecards with objectives for performance and risk management, including an according payroll process. A top-down capital-at-risk concept gives the executive board the desired control of the operative behaviour of all risk takers. It guarantees uniform compensations for business risks taken in any division or business area. The standard theory of cost-of-capital assumes standardized assets. Return distributions are equally normalized to a one-year risk horizon. It must be noted that risk measurement and management for any individual risk factor has a bottom-up design. The typical risk horizon for trading positions is 10 days, 1 month for treasury positions, 1 year for operational risks and even longer for credit risks. My contribution to the discussion is as follows: in the classical theory, one determines capital requirements and risk measurement using a top-down approach, without specifying market and regulation standards. In my thesis I show how to close the gap between bottom-up risk modelling and top-down capital alignment. I dedicate a separate paper to each risk factor and its application in risk capital management

Investigating Microinsurance Issues by Using Laboratory Experiments to Evaluate the Welfare of Insurance

This thesis uses laboratory experiments to develop a methodology to estimate the expected welfare benefits of insurance for individuals, conditional on their risk preferences. This methodology is then applied to study the welfare effects of issues that impact microinsurance, or insurance for the poor. The first result is that insurance take-up not a good proxy for the expected welfare gain of an individual’s choice to purchase or not to purchase insurance. The second result is that basis risk reduces the welfare obtained from index insurance. This welfare is significantly improved by having greater behavioral consistency with the Reduction of Compound Lotteries axiom. Finally, the risk of contract non-performance from the insurer significantly reduces the welfare obtained from insurance purchase decisions

Customer profitability forecasting using fair boosting : an application to the insurance industry

La prévision de la profitabilité du client, ainsi que la tarification, sont des pièces centrales dans le monde des sciences actuarielles. En utilisant des données sur les historiques des clients et en optimisant des modèles statistiques, les actuaires peuvent prévoir, dans une certaine mesure, le montant qu’un client réclamera durant une certaine période. Cependant, ces modèles utilisent souvent des données sensibles reliées au client qui sont considérées comme étant des facteurs de risque très importants dans la prédiction de pertes futures. Ceci est considéré comme étant légal dans plusieurs jurisdictions tant que leur utilisation est supportée par des données actuarielles, car ces attributs permettent aux clients d’obtenir une prime plus précise. Toutefois, comme soulevé dans la littérature récente en apprentissage machine, ces modèles peuvent cacher des biais qui les rendent discriminants envers certains groupes. Dans ce mémoire, nous proposons un modèle de prévision de la profitabilité du client utilisant des avancées récentes provenant du domaine de l’apprentissage machine pour assurer que ces algorithmes ne discriminent pas disproportionnellement envers certains sous-groupes faisant partie de l’intersection de plusieurs attributs protégés, tel que l’âge, la race, la religion et l’état civil. En d’autres mots, nous prédisons équitablement la prime théorique de n’importe quel client en combinant l’état de l’art en prédiction de pertes en assurance et appliquant certaines contraintes d’équité sur des modèles de régression. Suite à l’exécution de l’estimation de la profitabilité du client sur plusieurs jeux de données réels, les résultats obtenus de l’approche proposée sont plus précis que les modèles utilisés traditionnellement pour cette tâche, tout en satisfaisant des contraintes d’équité. Ceci montre que cette méthode est viable et peut être utilisée dans des scénarios concrets pour offrir des primes précises et équitables aux clients. Additionnellement, notre modèle, ainsi que notre application de contraintes d’équité, s’adapte facilement à l’utilisation d’un grand jeu de données qui contiennent plusieurs sous-groupes. Ceci peut être considérable dans le cas où un critère d’équité intersectionnel doit être respecté. Finalement, nous notons les différences entre l’équité actuarielle et les définitions d’équité provenant du monde de l’apprentissage machine, ainsi que les compromis reliés à ceux-ci.Customer profitability forecasting, along with ratemaking, are central pieces in the world of actuarial science. By using historical data and by optimising statistical models, actuaries can predict whether a client with certain liabilities will claim any loss and what amount will be claimed inside a defined policy period. However, these models often use sensitive attributesrelated to the customer that are considered to be crucial risk factors to consider in predicting future losses. This is considered legal in many jurisdictions, as long as their use is backedby actuarial data, as these attributes give a more accurate premium to clients. Nonetheless,as it has been noted in recent machine learning literature, models can hide biases that makethem discriminate against certain groups. In this thesis, we propose a customer profitability forecasting model that uses recent advancements in the domain of machine learning to ensurethat these algorithms do not discriminate disproportionately on a subgroup of any intersectionof protected attributes, such as age, gender, race, religion and marital status. In other words,we fairly predict the theoretical premium of any client by combining state-of-the-art methodsin insurance loss prediction and the application of fairness constraints on regression models. After performing customer profitability estimation on multiple real world datasets, it is shownthat the proposed approach outperforms traditional models usually used for this task, whilealso satisfying fairness constraints. This shows that this method is viable and can be used inreal world scenarios to offer fair and accurate premiums to clients. Additionally, our model andour application of fairness constraints scale easily when using large datasets that contain many subgroups. This can be substantial in the case of satisfying an intersectional fairness criterion.Finally, we highlight the differences between actuarial fairness and fairness definitions in theworld of machine learning, along with its related trade offs

Inventory Management with Raw Materials Costs Subject to Quotation: The Analysis of the Jewellery Industry

This thesis has the objective to present the particular inventory management problem in case of procurement of raw materials subject to quotation, a subject that goes beyond traditional stock control policies proposed by literature, where purchase price is typically assumed as a constant and therefore not even considered in the decision of when and how much to order

An empirical analysis and stochastic modelling of aggregate demand behaviour in a spare parts inventory system

The focus of the work here was an empirical analysis of the aggregate independent demand behaviour for spare parts inventories, principally in the automotive industry. In particular, using the pioneering work of RG Brown (1959), who showed that inventory usage values are often log normally distributed, we set out and developed models that go some considerable way to explaining the underlying stochastic basis for this phenomena, why it occurs and some limiting conditions. The justification for this approach was on the grounds that by providing a more fundamental understanding of the underlying stochastic processes that explain the emergent aggregate demand behaviour, a sound starting point would be provided for developing more sophisticated analytical ways to view an inventory range, as a total entity, for planning and control purposes. The analysis was based on extensive data collected from the DAF Trucks (GB) Ltd. spare parts systems spanning the period 1975 to 1986, together with supporting studies from a number of other systems. The analysis showed that in the systems studied spare parts prices are lognormally distributed and this is most likely to be the result of a stochastic process known as the 'theory of breakage'. Analysis also showed that in the DAF Trucks case aggregated and volumes in very short time periods are distributed as a combined Log Series /Negative Binomial distribution (LSD/NBD). The combined LSD/NBD model of aggregate demand volumes is itself fully explained by a stochastic model known as the Afwedson model, which in turn is derived from more elementary conditions based on the Poisson process. We then demonstrated that if these short period aggregate demand distributions are cumulated period by period they converge to a log normal distribution as the stable long run model of aggregate demand volumes. As a result of the lognormality of prices and volumes the resultant inventory usage values are also log normal. Furthermore from insight into the underlying factors that explain the lognormality we have identified the factors and variables that govern the valueso f the parameterso f the particular log normal models of usage values. - The research protocol used in this work incorporated the law verifying process know as 'retroduction' after work and discussions of Uji Ijiri and Herbert Simon (1977); and to a lesser extent we utilised simulation for validation and verification of the derived models. From the proven log normality of demand volumes and usage values we have demonstrated that a number of related key inventory factors are also lognormal, in particular inventory- item turnover rates. Furthermore our conclusions show that some standard inventory performance measures, such as the inventory wide 'stock turnover rate' and the 'stock to sales' ratio, are poor measures to use in the case of highly skewed inventory variables. Finally we have suggested several potentially fruitful areas for developing improved methods of monitoring inventory performance in a variety of circumstances