The Guaranteed Minimum Withdrawal Benefits (GMWBs) are optional riders provided by insurance companies in variable annuities. They guarantee the policyholders' ability to get the initial investment back by making periodic withdrawals regardless of the impact of poor market performance. With GMWBs attached, variable annuities become more attractive. This type of guarantee can be challenging to price and hedge. We employ two approaches to price GMWBs. Under the constant static withdrawal assumption, the first approach is to decompose the GMWB and the variable annuity into an arithmetic average strike Asian call option and an annuity certain. The second approach is to treat the GMWB alone as a put option whose maturity and payoff are random. Hedging helps insurers specify and manage the risks of writing GMWBs, as well as find their fair prices. We propose semi-static hedging strategies that offer several advantages over dynamic hedging. The idea is to construct a portfolio of European options that replicate the conditional expected GMWB liability in a short time period, and update the portfolio after the options expire. This strategy requires fewer portfolio adjustments, and outperforms the dynamic strategy when there are random jumps in the underlying price. We also extend the semi-static hedging strategies to the Heston stochastic volatility model.

A simulation game was designed to examine the impact of a guaranteed annual income (GAI). The sample of 158 player-objects included factory and clerical workers, high school dropouts, single mothers, and CEGEP and university social work students. To establish the validity of the game, the working and spending behaviour of players was compared with results reported for the New Jersey negative income tax experiment, and found to be similar in a number of respects. The game also simulated two features not present in the New Jersey experiment: (a) variable labour-market conditions, and (b) comparison of a partial, time-limited GAI with a permanent, universal plan. For players on a GAI, working hours were significantly lower when fellow-players were not on a GAI than when they were. Results suggest that work effort may be related to comparisions with a reference group on visible consumer goods.

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1962. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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Ce mémoire présente une approche basée sur des méthodes garanties pour résoudre des problèmes d’optimisation de systèmes dynamiques multi-physiques. Ces systèmes trouvent des applications directes dans des domaines variés tels que la conception en ingéniérie, la modélisation de réactions chimiques, la simulation de systèmes biologiques ou la prédiction de la performance sportive.La résolution de ces problèmes d’optimisation s’effectue en deux phases. La première consiste à mettre le problème en équations sous forme d’un modèle mathématique constitué d’un ensemble de variables, d’un ensemble de contraintes algébriques et fonctionelles ainsi que de fonctions de coût. Celles-ci sont utilisées lors de la seconde phase qui consiste à d’extraire du modèle les solutions optimales selon plusieurs critères (volume, poids, etc).Les contraintes algébriques permettent de manipuler des grandeurs statiques (quantité, taille, densité, etc). Elles sont non linéaires, non convexes et parfois discontinues.Les contraintes fonctionnelles permettent de manipuler des grandeurs dynamiques. Ces contraintes peuvent être relativement simples comme la monotonie ou la périodicité, mais aussi bien plus complexe par la prise en compte de contraintes différentielles simples ou définies par morceaux. Les équations différentielles sont utilisées pour modéliser des comportements physico-chimiques (magnétiques, thermiques, etc) et d’autres caractéristiques qui varient lors de l’évolution du système.Il existe plusieurs niveaux d’approximation pour chacune de ces deux phases. Ces approximations donnent des résultats pertinents, mais elles ne permettent pas de garantir l’optimalité ni la réalisabilité des solutions.Après avoir présenté un ensemble de méthodes garanties permettant de résoudre de manière garantie des équations différentielles ordinaires, nous formalisons un modèle particulier de systèmes hybrides sous la forme d’équations différentielles ordinaires par morceaux. A l’aide de plusieurs preuves et théorèmes nous étendons la première méthode de résolution pour résoudre de manière garantie ces équations différentielles par morceaux. Dans un second temps, nous intégrons ces deux méthodes au sein d’un module de programmation par contracteurs, que nous avons implémenté. Ce module basé sur des méthodes garantie permet de résoudre des problèmes de satisfaction de contraintes algébriques et fonctionnelles. Ce module est finalement utilisé dans un algorithme d’optimisation globale déterministe modulaire permettant de résoudre les problèmes considérés. / In this thesis a set of tools based on guaranteed methods are presented in order to solve multi-physics dynamic problems. These systems can be applied in various domains such that engineering design process, model of chemical reactions, simulation of biological systems or even to predict athletic performances.The resolution of these optimization problems is made of two stages. The first one consists in defining a mathematical model by setting up the equations for the problem. The model is made of a set of variables, a set of algebraic and functional constraints and cost functions. The latter are used in the second stage in order to extract the optimal solutions from the model depending on several criteria (volume, weight, etc).Algebraic constraints are used to describe the static properties of the system (quantity, size, density, etc). They are non-linear, non-convex and sometimes discontinuous. Functional constraints are used to manipulate dynamic quantities. These constraints can be quite simple such as monotony or periodicity or they can be more complex such as simple or piecewise differential constraints. Differential equations are used to describe physico-chemical properties (magnetic, thermal, etc) and other features evolving with the component use. Several levels of approximation exist for each of these two stages. These approximations give some relevant results but they do not guarantee the feasibility nor the optimality of the solutions.After presenting a set of guaranteed methods in order to perform the guaranteed integration of ordinary differential equations, a peculiar type of hybrid system that can be modeled with piecewise ordinary differential equation is considered. A new method that computes guaranteed integration of these piecewise ordinary differential equations is developed through an extension of the initial algorithm based on several proofs and theorems. In a second step these algorithms are gathered within a contractor programming module that have been implemented. It is used to solve algebraic and functional constraint satisfaction problems with guaranteed methods. Finally, the considered optimization problems are solved with a modular deterministic global optimization algorithm that uses the previous modules.

Existing multi-echelon inventory optimization models and formulas were studied to get an understanding of how safety stock levels are determined. Because of the restrictive distribution assumptions of the existing safety stock formula, which are not necessarily realistic in practice, a method to analyze the performance of this formula in a more realistic setting was desired. A SimPy simulation model was designed and implemented for a simple two-stage supply chain as a way to test the performance of the safety stock formula. This implementation produced results which led to the conclusion that the safety stock formula tends to underestimate the level of safety stock needed to provide a certain service level when predicted standard deviation of demand is underestimated and the assumptions of normally distributed demand and normally distributed lead times are not fulfilled.

Since small and medium ¡Vsize enterprises (SMEs) have played a fundamental role in the economic development of this country, as a intermediary, the financial assistance of Taiwan SMEG to SMEs, is the greatest contribution to the above, nevertheless, Taiwan SMEG has been immersing in a predicament of financial deficit due to the unbalanced budget for a long time. Except the Package Credit Guarantee has introduced the concept of total risk control, all the others like the Authorized Approach and the Normal Approach have not introduced yet. For its perennial operation, Taiwan SMEG must set up an appropriate system for the rate of guarantee fees to achieve self-contained and self-sufficient condition, also to obtain the best efficiency under its limited resources. This paper uses the market ¡Vbased risk neutral model developed by Kuo (2006) to estimate the probability of default of banking loan assets through the risk premium of each banking loan, further to stimulate the guarantee fees by using the actuarial valuation principles. The purpose of this model is to react the degree of credit risk on the stimulated guarantee fees , making the fees pricing mechanism reasonable and fair . The model also analyzed the cost of subrogation payment under default cases by different industry , making it a reference for banks and Taiwan SMEG. The empirical results show that: 1.The credit guarantee fees stimulated by this model are approximately fair comparative to the actual subrogation payments of default cases reimbursed by Taiwan SMEG. The result provide evidence that the model possess the power of fitness for estimating the default cost of subrogation payment. 2.The degree of credit risk can actually react on the guarantee fees through using this model. It is essential to set up different range for rate of guarantee fees according to the subrogation payment ratio of default cost caused by respective guaranteed industry. The result suggests that Taiwan SMEG should amplify the extreme energy of guarantee through reasonable and fair use of its limited resources. Using the data of Taiwan SMEG guaranteed cases, this paper also analysis the default cost between the cost of funds and earning profits for the banking loans. The banks in Taiwan earn less profits than before under the overbanking environment. The competitive bank¡¦s loan pricing strategy leads to extreme loss while the default cases occur. In the lights of risk management , banks have become a high risk and low return industry. It is essential for banks to emphasize the loan quality and pricing strategy when expanding their loan business. Banks must simultaneously evaluate the RAROC under a perfect risk management system, so that the monetary environment can be improved and banks can take advantage of it by earning reasonable profits.

Product risk is important to firms’ enterprise risk management. This dissertation focuses on product risk in the U.S. life insurance and health insurance industries. In particular, we add new dimensions to the measurement of product risk for these industries, and we explore how these industries manage product risk in a context of other enterprise risks. In this dissertation, we identify new product risks, propose new measures, and study the management of these risks. In the life insurance industry, we identify a new type of product risk, the guarantee risk, caused by variable annuities with guaranteed living benefits (VAGLB). We propose a value-at-risk type measure inspired by the risk-based capital C3 Phase II to quantify the guarantee risk. In the health insurance industry, where the degree of uncertainty varies for different types of health insurance policies, we develop four exposure-based risk measures to capture health insurers’ product risks. Then we study how life and health insurers manage product risks (and asset risks) by using capital in the context of other risks and appropriate controls. We add to the literature in the life insurance industry by examining the relationship between capital and risks when the guarantee risk is accounted for. In the health insurance industry, to our knowledge, no similar research on the relationship between capital and risks has been conducted. In view of the current topicality of health insurance, our research therefore adds a timely contribution to the understanding of health insurer risk management in an era of health care reform. Capital structure theories, transaction cost economics, and insurers’ risk-taking behaviors provide the theoretical foundation for our research. As to methodology, we implement standard capital structure models for the life and health insurance industries using data from the National Association of Insurance Commissioners (NAIC) annual filings of life/health insurers and health insurers. Simultaneous equations modeling is used to model life and health insurers’ enterprise risk management. And the estimation is conducted by the generalized estimation equations (GEE). We find that both U.S. life/health insurers and health insurers prudently build up capital as they experience more product risk and asset risk controlling for the other enterprise risks. We also find that life/health insurers may be using derivatives as a partial substitute for capital when managing new product risk caused by VAGLB, the guarantee risk. / text