Honors Projects in Mathematics

A Study of Women Working in the Actuarial Field

Jillian Emberg — Mon, 25 Mar 2013 20:48:18 PDT

The goal of this project is to examine how women fit into the actuarial career path and how cultural expectations, biological factors, and personal aspirations affect their experiences in the field. Dramatic changes in the profession have occurred since its emergence in the nineteenth century to become more welcoming to women who choose to enter the profession. However, despite the equalizing demographic shifts of the field, it is still a male-dominated profession. This paper attempts to analyze why some of the changes in the demographics of the field have occurred as well as explain what factors contribute to women’s underrepresentation as actuarial professionals by referring to previous research regarding gender roles in mathematics, which arguably arise from both biological and sociological sources. To help tie these arguments into the specific field of actuarial mathematics, an independent survey was administered to current and former actuaries that tested their beliefs about the degree to which gender can influence success in the actuarial field, and the results were compared to existing theories about women in mathematics. The survey participants were selected using the names from the online data base ActuarialDirectory.org as well as using a list of Bryant Alums who graduated with a degree in Actuarial Sciences that was provided from Bryant’s Alumni Network. The test results were analyzed using two tail t-tests, and further detail about the testing processes can be found in appendix C.

Are NFL Athletes Receiving Over-Valued Contracts?

Jason Scott — Sun, 24 Mar 2013 20:48:55 PDT

Many sport research studies have been conducted that examine the performance of professional athletes and their corresponding effect on franchise winning percentages, team revenues, economic repercussions, performance-based compensation, and much more. Research in the National Football League, however, has been found to be somewhat limited due to the numerous possible positions and resulting vastness of position-specific variables. The NFL lockout in 2011 caused many to question the specific relationship between professional athlete performance and salary distribution. This study’s purpose was to find a collection of variables with which all NFL athletes could be compared, and to identify relationships existing between a player’s performance and his value/salary. Data was collected from USAToday.com, Pro-football-reference.com, and AdvancedNFLStats.com. This data was then organized and manipulated into a format that allowed all players in the league during the 2009 season to be compared. Of the nine variables considered for this study, four were found to have a significant relationship with a player’s value/salary. These results were utilized to create a Player Valuation model and then analyze the overall salary distribution throughout the NFL. From this, it was observed while there are many athletes in the NFL that receive extravagant salaries well over their projected value, there is a much larger portion of the league that is undervalued and receive less than their projected value. It was then concluded that a super-star variable would be necessary to create a more accurate Player Valuation model, and the reason there is a larger proportion of NFL players receiving a lower salary than they deserve is due to franchise cap limits. These cap limits place pressure on franchises to push down the salaries of non-superstar athletes in order to compensate for the salaries required for the super-star athletes on their rosters.

Factors Related to Math Performance and Potential Benefits of One-on-One Instruction

Amanda Zagame — Thu, 10 Nov 2011 19:54:43 PST

This fall 2010 study of Bryant University students enrolled in freshman-level math courses considered factors related to college-level math performance, including gender, math self-efficacy, math anxiety, and utilization of professors’ office hours and/or tutoring center services. Female students at Bryant reported lower levels of math self-efficacy and higher levels of math anxiety, both of which research has shown to be negatively correlated with test scores. The use of one-on-one instruction was expected to provide a potential counterweight to this equation. Results from the 287 initial and 229 final surveys administered in this study did not support this hypothesis. This phenomenon was interpreted and potential solutions to the gender problem in mathematics were explored.

A Multiple Regression Analysis of Personality’s Impact on Actuarial Exam Performance

Matthew Ciaffone — Wed, 02 Nov 2011 16:03:16 PDT

Existing literature indicates that there is some connection between personality and both academic and work-related performance. The author's intent for the research described herein is to explore this connection for students majoring in actuarial mathematics with regard to their performance on actuarial certification exams. Specifically, using the five-factor model of personality, the author seeks to predict the number of attempts required to pass the first two exams in the process (Exam 1/P - probability; Exam 2/FM - financial mathematics) using measures of the five dimensions of the five-factor model (openness to experience, conscientiousness, extraversion, agreeableness, and emotional stability) through regression analysis. The author also examined the same variables’ effect on a binary passing indicator. The sample consists of 100 actuarial mathematics majors at three universities in southern New England. Although the results are not conclusive, it appears that conscientiousness correlates positively with performance and neuroticism correlates negatively with performance. In the future, the author suggests research with a larger sample size and an examination of non-linear relationships.

Determining the Success of NCAA Basketball Teams through Team Characteristics

Raymond Witkos — Wed, 13 Apr 2011 20:54:15 PDT

Every year much of the nation becomes engulfed in the NCAA basketball postseason tournament more affectionately known as “March Madness.” The tournament has received the name because of the ability for any team to win a single game and advance to the next round. The purpose of this study is to determine whether concrete statistical measures can be used to predict the final outcome of the tournament. The data collected in the study include 13 independent variables ranging from the 2003-2004 season up until the current 2009-2010 season. Different tests were run in an attempt to achieve the most accurate predictive model. First, the data were input into Excel and ordinary least squares regressions were run for each year. Then the data were compiled into one file and an ordinary least squares regression was run on that collection of data in Excel. Next, the data were input into Minitab and a stepwise regression was run in order to keep only the significant independent variables. Following that, a regression analysis was run in Minitab. The coefficients from that regression analysis were input into a file with the 2009-2010 data in an attempt to test the model’s results against the actual results. All of the models developed, except one for the year 2005-2006, were determined to be significant. There were 6 significant independent variables determined. The final results showed that although the model developed through the study was significant, the ability to accurately predict the outcomes is very difficult.

Predictive Modeling of Alumni Donor Behavior

Lauren Prue — Tue, 12 Apr 2011 20:52:47 PDT

In recent years, college and universities have relied increasingly upon the charitable contributions of its previous graduates; as the costs of tuition rise substantially, development offices are facing the challenge of creating annual fund campaigns that are minimally expensive while providing the maximum potential for return. This study addresses the available constituent database at one University in particular in an effort to identify what criteria are the strongest predictors of donor response at a small, private university located within New England. The analysis utilized predictive modeling and data-mining largely within the software program Rapid Insight to build several models in an effort to streamline the soliciting process and identify constituents with the highest propensity to donate at a variety of levels.

The analysis includes statistical models intended to identify which characteristics make an individual likely to transition from non-donor to donor status, what ask techniques are most successful for a philanthropic campaign, which individuals are most likely to provide large donations, and which individuals will give consecutive gifts over several years. Statistical modeling builds on current research within the field of university development office data mining; it serves as an evaluation of several studies that indicate that a negative growth rate in giving occurs around the retirement age; this does not appear to be the case at this particular institution. In addition, it builds upon evidence suggesting which majors at predominantly business colleges have the strongest likelihood of providing large gifts to their alma mater. Several models within the study suggest which solicit techniques have the strongest success rate for a philanthropic campaign, including the use of telefund calls, direct mail solicits, e-mail solicits, and several other possibilities.

A Statistical Analysis of Defined Benefit, Defined Contribution, and Hybrid Plans

Katie Heeder — Thu, 07 Apr 2011 20:02:10 PDT

The purpose of this study is to compare three major types of employer sponsored retirement plans, Defined Benefit (DB), Defined Contribution (DC), and hybrid, and their impact on the employee. Employee careers are simulated to understand the employee’s advantages and disadvantages of each type of plan, especially in the state of an economic depression. The study uses actuarial assumptions and the simulation varies a number of quantities to better understand the impact of employee savings. The variables which are simulated at different levels are: service start age, retirement age, current compensation, salary increase rate, rate of return on market investments, mortality rates, and interest rate. The simulation shows that traditional defined benefit plans typically give employees a higher benefit than both defined contribution and hybrid plans. Additionally, defined benefit plans are not subject to the market risk of many of the other retirement plan types. Finally, typical employees change plans at least once during their career and this has a significant negative effect on their retirement benefits.

The Discriminant Analysis Used by the IRS to Predict Profitable Individual Tax Return Audits

Amber Torrey — Wed, 08 Oct 2008 17:08:01 PDT

This paper discusses past and current methods the IRS uses to determine which individual income tax returns to audit. The IRS currently uses the discriminant function to give all individual tax returns two scores; one based on whether it should be audited or not and one based on if the return is likely to have unreported income. The discriminant function is determined by the IRS’s National Research Program, which takes a sample of returns and ensures their accuracy. Previously, the function was determined by the IRS’s Taxpayer Compliance Measurement Program. However, this was too burdensome and time consuming for taxpayers. The data mining techniques of decision trees, regression, and neural networks were researched to determine if the IRS should change its method. Unfortunately IRS tax data were not obtainable due to their confidentiality; therefore credit data from a German bank was used to compare discriminant analysis results to the three new methods. All of the methods were run to predict creditworthiness and were compared based on misclassification rates. The neural network had the best classification rate closely followed by regression, the decision tree, and then discriminant analysis. Since this comparison is not based on IRS tax data, no conclusion can be made whether the IRS should change its method or not, but because all methods had very close classification rates, it would be worthwhile for the IRS to look into them.