Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 73-77). Also available in print.

Retirement security for Americans is one of the most critical public policy and personal financial issues and will be for decades in the future. Individuals that retire today can live an additional 30 or even 40 years with less secure income as corporations shift to defined contribution plans to fund retirement. Based on the life cycle savings hypothesis, immediate annuities should be appealing to retirees because they insure against the risks of outliving retirement assets by converting funds into a lifelong stream of income. However, research has found that retirees are reluctant to annuitize their wealth. This study examined the attitudes of Utah State University employees toward annuitization of retirement assets and explored the relationship between employee characteristics and their attitudes toward immediate annuities. Data for this study were collected through an online questionnaire emailed to Utah State University employees who participate in a defined contribution plan. The survey gathered information on retirement portfolio losses, expected longevity, financial confidence, familiarity with annuities, and attitudes toward immediate annuities. A total of 744 individuals answered the survey for a response rate of 43.2%. Based on the results of independent t tests, there were statistically significant differences between the attitudes of women and men toward immediate annuities. Women held more positive attitudes toward immediate annuities than men, and women who had taken a retirement planning class had more positive attitudes than women who had not attended a retirement class. In contrast, men who had attended a retirement class expressed less positive attitudes toward immediate annuities than men who had not. Male overconfidence in their investment knowledge and skills may explain this finding. A Pearson correlation coefficient revealed a negative correlation between risk aversion and attitudes toward annuities. As investment risk tolerance decreases, attitudes toward immediate annuities become more positive. An analysis of variance found that individuals with longer than average life expectancies had more positive attitudes toward immediate annuities than subjects with shorter than average life expectancies. Surprisingly, individuals who claimed to be most familiar with immediate annuities showed the least positive attitudes toward annuities. Income and assets, marital status, and financial confidence were not statistically significantly related to attitudes toward annuities. Implications for consumers, financial professionals, educators, and policymakers were drawn from the results of the study.

Thesis (MComm)--Stellenbosch University, 2013. / In this thesis, based on historical data, a comparative study is conducted of various annuity strategies for South African males who retired during the 30 years from 1960 to 1989. To this end, the present values of the monthly cash ows provided by di erent annuity strategies are calculated and compared in order to ascertain which strategy would have provided the largest nancial bene ts. In contrast to previously held general beliefs, the calculations demonstrate that pure living annuity strategies are superior to composite annuity strategies, which in turn outperform switching annuity strategies, whereas pure life annuities yield the lowest return.

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

The first chapter (with Richard Arnott) considers an atomistic developer who decides when and at what density to develop his land, under a property value tax system characterized by three time-invariant tax rates. The second chapter adds to the controversial literature on private annuities. The third chapter examines whether a parent's illness causes adult children to provide their parents with financial assistance. / Thesis (PhD) — Boston College, 2004. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

本研究主要探討附保證最低提 (Guaranteed Minimum Withdrawal Benefits, GMWB)的變額(Variable Annuity, VA) 在隨機模型下之定價。保證最低提是變額的一種附加約 (rider) 並在市場下跌的情況下為變額持有人提供保障。它保證持有人在合約期內的總提少於一個預先訂的額，而變額的投資表現。一般，這個保證額相等於變額的初始投資額。本研究的融模型假設投資標的基價格符合對維過程 (exponential Lévy process)，而隨機則符合由維過程驅動的瓦西克模型 (Vasiček model)。融模型中的個維過程的相依結構 (dependence structure) 會由維關結構 (Lévy Copula) 描述。這個方法的好處是可描述同型的相依結構。用一個配合維關結構而有效的蒙地卡模擬方法，我們研究在同相依結構及模型下保證最低提的價值變化。在固定的特別情況下，保證最低提的價值能夠透過卷積方法 (convolution method) 而得到半解析解 (semi-analytical solution) 。最後，我們將本研究中的學模型擴展以研究近期出現由保證最低提演化而成的一種保證產品。這個產品名稱為保證終身提 (Guaranteed Lifelong Withdrawal Benefit, GLWB)，而此產品的到期日則與持有人的壽命相關。 / In this thesis, we study the problem of pricing the variable annuity(VA) with the Guaranteed Minimum Withdrawal Benefits (GMWB) under the stochastic interest rate framework. The GMWB is a rider that can be elected to supplement a VA. It provides downside protection to policyholders by guaranteeing the total withdrawals throughout the life of the contract to be not less than a pre-specied amount, usually the initial lump sum investment, regardless of the investment performance of the VA. In our nancial model, we employ an exponential L´evy model for the underlying fund process and a Vasiček type model driven by a L´evy process for the interest rate dynamic. The dependence structure between the two driving L´evy processes is modeledby the L´evy copula approach whichis exible to model a wide range of dependence structure. An effcient simulation algorithm on L´evy copula is then used to study the behavior of the value of the GMWB when the dependence structure of the two L´evy processes and model parameters Vry. When the interest rate is deterministic, the value of the GMWB can be solved semi-analytically by the convolution method. Finally, we extend our model to study a recent variation of GMWB called Guaranteed Life long Withdrawal Benefits (GLWB) in which the maturity of the GLWB depends on the life of the policyhodler. / Detailed summary in vernacular field only. / Chan, Wang Ngai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 115-121). / Abstracts also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Variable Annuity & Guaranteed Minimum Withdrawal Benefit --- p.1 / Chapter 1.2 --- Literature Review --- p.4 / Chapter 1.3 --- Financial Model for GMWB --- p.7 / Chapter 2 --- L´evy Copulas and the Simulation Algorithm --- p.12 / Chapter 2.1 --- Definitions and Theorem --- p.15 / Chapter 2.2 --- Examples of L´evy Copulas --- p.19 / Chapter 2.2.1 --- Independence case --- p.19 / Chapter 2.2.2 --- Complete Dependence --- p.20 / Chapter 2.2.3 --- The Clayton L´evy Copula --- p.21 / Chapter 2.3 --- Simulation algorithm for two-dimensional dependent L´evy process --- p.22 / Chapter 3 --- Model Formulation for GMWB --- p.26 / Chapter 3.1 --- Financial Model for GMWB --- p.27 / Chapter 3.2 --- Underlying Fund of VA and the Interest Rate --- p.30 / Chapter 3.3 --- A Special Case of Deterministic Interest Rate --- p.34 / Chapter 4 --- Numerical Implementation --- p.38 / Chapter 4.1 --- The Clayton L´evy Copula --- p.39 / Chapter 4.2 --- The Underlying Fund and the Interest Rate Processes --- p.42 / Chapter 4.3 --- Kendall’s Tau Coefficient --- p.47 / Chapter 4.4 --- The GMWB Option Value --- p.49 / Chapter 4.4.1 --- Control Variate for Simulation --- p.49 / Chapter 4.4.2 --- Simulation Results --- p.51 / Chapter 4.5 --- Deterministic Interest Rate --- p.52 / Chapter 5 --- GMWB Pricing Behavior --- p.56 / Chapter 5.1 --- L´evy model for the underlying fund --- p.57 / Chapter 5.1.1 --- The Skewness --- p.57 / Chapter 5.1.2 --- The Kurtosis --- p.65 / Chapter 5.2 --- The Vasiček model driven by L´evy process --- p.73 / Chapter 5.2.1 --- The Volatility Parameter ôV --- p.73 / Chapter 5.2.2 --- The Mean Reverting Parameter aV --- p.77 / Chapter 5.3 --- Dependence between the underlying fund and rate processes --- p.81 / Chapter 5.3.1 --- The jump direction dependence parameter n{U+1D9C} --- p.83 / Chapter 5.3.2 --- The jump magnitude dependence parameter θ{U+1D9C} --- p.90 / Chapter 6 --- GMWB for Life --- p.96 / Chapter 6.1 --- Model Formulation --- p.98 / Chapter 6.1.1 --- Mortality model --- p.99 / Chapter 6.1.2 --- Financial Model for GLWB --- p.101 / Chapter 6.2 --- GLWB product from John Hancock --- p.103 / Chapter 6.3 --- GLWB Pricing Behavior --- p.104 / Chapter 6.3.1 --- The correlation effect --- p.106 / Chapter 7 --- Conclusion --- p.108 / A Proofs --- p.113 / Chapter A.1 --- Proof of Equation 3.1 --- p.113 / Chapter A.2 --- Proof of Equation 3.3 --- p.114 / Bibliography --- p.115

Several of the more complex optimization problems in finance can be characterized as impulse control problems. Impulse control problems can be written as quasi-variational inequalities, which are then solved to determine the optimal control strategy. Since most quasi-variational inequalities do not have analytical solutions, numerical methods are generally used in the solution process. In this thesis, the impulse control problem framework is applied to value two complex long-term option-type contracts. Both pricing problems considered are cast as impulse control problems and solved using an implicit approach based on either the penalty method or the operator splitting scheme. The first contract chosen is an exotic employee stock option referred to as an infinite reload option. This contract provides the owner with an infinite number of reload opportunities. Each time a reload occurs, the owner pays the strike price using pre-owned company shares and, in return, receives one share for each option exercised and a portion of a new reload option. Numerical methods based on the classic Black-Scholes equation are developed while taking into account contract features such as vesting periods. In addition, the value of an infinite reload option to it's owner is obtained by using a utility maximization approach. The second long-term contract considered is a variable annuity with a guaranteed minimum death benefit (GMDB) clause. Numerical methods are developed to determine the cost of the GMDB clause while including features such as partial withdrawals. The pricing model is then used to determine the fair insurance charge which minimizes the cost of the contract to the issuer. Due to the long maturity of variable annuities, non-constant market parameters expressed through the use of regime-switching are included in the GMDB pricing model.

Several of the more complex optimization problems in finance can be characterized as impulse control problems. Impulse control problems can be written as quasi-variational inequalities, which are then solved to determine the optimal control strategy. Since most quasi-variational inequalities do not have analytical solutions, numerical methods are generally used in the solution process. In this thesis, the impulse control problem framework is applied to value two complex long-term option-type contracts. Both pricing problems considered are cast as impulse control problems and solved using an implicit approach based on either the penalty method or the operator splitting scheme. The first contract chosen is an exotic employee stock option referred to as an infinite reload option. This contract provides the owner with an infinite number of reload opportunities. Each time a reload occurs, the owner pays the strike price using pre-owned company shares and, in return, receives one share for each option exercised and a portion of a new reload option. Numerical methods based on the classic Black-Scholes equation are developed while taking into account contract features such as vesting periods. In addition, the value of an infinite reload option to it's owner is obtained by using a utility maximization approach. The second long-term contract considered is a variable annuity with a guaranteed minimum death benefit (GMDB) clause. Numerical methods are developed to determine the cost of the GMDB clause while including features such as partial withdrawals. The pricing model is then used to determine the fair insurance charge which minimizes the cost of the contract to the issuer. Due to the long maturity of variable annuities, non-constant market parameters expressed through the use of regime-switching are included in the GMDB pricing model.

Entre 1769 et 1789 le roi de France a émis des emprunts viagers et des tontines à des taux réels très supérieurs à ceux qu’il autorisait aux particuliers. Il l’a fait en connaissance de cause en offrant une prime de risque palliant la faiblesse de sa signature. Celle-ci était masquée par l’absence de table de mortalité et de tarif reconnus. Marginaux à l’origine, ces emprunts ont eu une première importance lors de la guerre de succession d’Espagne avec des rentes mixtes puis avec la consolidation des années 1720. Après une période de petits emprunts en classes d’âges, Ils sont revenus au premier plan des moyens d’endettement pendant la guerre de sept ans lorsque, en négligeant la table de Deparcieux, le roi emprunta en viager à un taux uniforme lors d’emprunts massifs, afin de capter les placements sur des têtes jeunes. Leur importance perdura après le conflit, et ils sont devenus un outil majeur des décennies suivantes, à l’impact financier croissant, par paix comme par guerre, au point de tenir le premier plan dans la dette publique à la veille de la révolution.Alors que genevois, génois et hollandais maitrisaient les règles rudimentaires de la mortalité et optimisaient avec plus ou moins d’efficacité leurs mises dans le viager de France, les nationaux ont ignoré les excellents apports académiques français dans ce domaine et, à l’exception des manieurs d’argent, ont eu un comportement bien moins efficace, aussi bien dans les emprunts publics que privés.Le viager a présenté les avantages et les inconvénients d’un marché trouble, où l’absence de règles affichées permet au roi comme aux particuliers de payer des primes de risque sans le montrer, mais où les personnes âgées sont lésées, et où ceux qui doivent revendre les contrats achetés ne peuvent le faire qu’à prix cassé.La progression du recours de l’état à ces emprunts n’est pas une marque d’incompétence mais d’une dégradation de son crédit pendant les trente ans qui précèdent la révolution, liée à un manque de ressource fiscale. / Between 1689 and 1789 France issued life annuities and tontines at true rates above what was permitted to private persons. This was made with plain knowledge by offering a risk premium palliating its weak creditworthiness, hidden by the absence of mortality table or accepted life annuities rates. Marginal at the beginning, these loans took a first importance during the war of Spanish succession with mixed annuities, then with the consolidation operations of the 1720s. After a period of small age-group loans, they came back at the forefront of ways to borrow during the seven years war when, neglecting Deparcieux’s life table, the king started to borrow at a uniform life rate in massive loans, trying to catch investments on young people. Their importance continued after this conflict, and they became a major tool for subsequent decades, with an increasing financial impact, by wartime like by peace, reaching the first rank of public debt at the eve of the revolution.Meanwhile Genevan, Genoese, and Dutch mastered the basic rules of mortality and optimized their investments in french life annuities with more or less efficiency, the nationals overlooked french first-class academic contributions in this field and, apart the business community, had far less efficient behaviours, as well for public or private loans.Life annuities had advantages and disadvantages of a murky market, where the lack of apparent rules allows the king or private person to pay risk premium without showing it, but where aged people suffer damage, and where those who have to assign their contract can do it only at a rock-bottom price.The progressive appeal of state at these toxic loans does not mean ineptitude but a heightening credit risk during the thirty years preceding the revolution, linked to a lack of tax based resource.

The thesis is concerned with the problem of sustainable spending towards the end of the human life cycle, which is a substantial quantitative problem in the pension framework. We gradually build a model, which coherently links the three key factors of retirement planning: uncertain length of human life, uncertain investment returns and spending rates. Within the framework of our intuitive model, we apply the method of moment matching to derive an approximation for the probability of individual's retirement ruin. The accuracy of presented approximation is analyzed via extensive Monte Carlo simulations. A numerical case study using Czech data is provided, including calculated values for the probability of ruin and maximal sustainable spending rate under various combinations of wealth-to-spending ratios and investment portfolio characteristics.