An Invitation to Undergraduate Research in Risk Management

Inhaltsverzeichnis

1. Frontmatter

2. Gaussian Processes for Statistical Learning in Actuarial Science

   Mike Ludkovski, Jimmy Risk

   Abstract

   This chapter explores statistical learning, spotlighting the role of Gaussian process (GP) models. It initiates with a foundational exposition on data-driven curve fitting, focusing on probabilistic modeling via GP regression. We especially highlight the role of GP kernels and GP mean functions on the fit. The chapter provides two extended case studies rooted in actuarial applications: mortality rate modeling and variable annuity valuation. Analysis is illustrated with a plenty of figures and results, and the chapter is supplemented by a companion Github repository so that users can get hands-on engagement through the provided Python and R notebooks. The outlined research projects serve as conduits for students to deepen their understanding and better navigate the multifaceted aspects of the actuarial applications.

3. What Benefits Drive Membership in Medicare Advantage Plans?

   Ian Duncan, Juan Diego Mejia Becerra, Jiarui Yu

   Abstract

   The objective in this chapter is to identify the most relevant benefits of medicare advantage health plans that drive membership and market share. We explore plans operating in Connecticut from September 2019 to 2022. A dataset of benefits from publicly available data sources is created for this chapter, and PCR is applied to capture the correlation between the extracted features and market share, avoiding the multicollinearity and overparameterization problems. We identify a degree of correlation between market share and prominent benefits and features such as drug coverage, star ratings, and dietary benefits, among others.

4. Pricing Variable Annuity Guarantees Using Monte Carlo Simulations

   Thorsten Moenig

   Abstract

   Variable annuities (VAs) are highly popular retirement savings products sold by U.S. life insurance companies. They include complex long-term financial guarantees which offer unique protections for investors while creating interesting challenges for providers. In this chapter, we learn how to price and value these guarantees using Monte Carlo simulations. We begin by exploring how to simulate random stock price movements (based on lognormal distributions). I then provide an introduction to financial options and illustrate how to use these simulated scenarios to price all kinds of options, which ultimately also includes VA guarantees. After a brief introduction to VAs, I show how to value maturity, death, and withdrawal benefit guarantees using simulation. I close the chapter by proposing a series of research questions for the reader to explore.

5. Modeling Volatility in Finance

   Gábor Francsics

   Abstract

   Our goal in this chapter is to explore a method to construct arbitrage-free parametric volatility surfaces. Volatility surfaces play a very important role in pricing financial derivative securities on option markets. After the necessary background information and preliminary exercises, we guide the students and their mentors to the point where they can explore further research projects and open problems using real empirical data.

6. Introduction to Fixed-Income Markets and Bonds

   Gareth W. Peters, Sooie-Hoe Loke

   Abstract

   This chapter will provide an overview of several core concepts relating to fixed-income markets. In particular, the reader will be familiarized with a working knowledge of the following: What is a bond instrument and its basic components; forward rates, interest yields, and yield; bond price relationships including the conversion of a coupon paying bonds to zero-coupon bonds; risk quantification for fixed-income settings; as well as where to find data for modeling of interest rates from various countries. The reader will also be exposed to the technique of constructing a yield curve using bootstrapping and spline interpolation.

7. Essential Aspects of Bayesian Data Imputation

   William Holt, Duy Nguyen

   Abstract

   Data imputation holds significant importance in a variety of fields including risk management. Incomplete or missing data can hinder a thorough analysis of risks, making accurate decision-making challenging. By employing imputation techniques to fill in the gaps, risk managers can obtain a more comprehensive and reliable understanding of the underlying risk factors. This, in turn, enables them to make informed decisions and develop effective strategies for risk mitigation. This note introduces the concept Bayesian data imputation. We collect and provide backgrounds needed for Bayesian data imputation when missing data are missing at random. Numerical examples are provided for demonstration.

8. An Introduction to Sports Analytics Research with Expected Goals

   Ronald Yurko

   Abstract

   Sports analytics is a growing field with many avenues and entry points for students to engage in research projects. In this chapter, we demonstrate relevant topics and skills through the development of an expected goals model in hockey. Through this simple example, we discuss estimating the expected value of an action in sports by building a logistic regression model that is well-calibrated out-of-sample. This brings to attention unique aspects of sports data that must be taken into consideration for cross-validation procedures. Once the reader is comfortable with this model, we discuss how it can be used for evaluating team and player performance. This motivates the direction for introducing a hierarchical model to account for player effects, which is a fundamental method prevalent throughout sports analytics research. Finally, we emphasize the importance in measuring uncertainty of model estimates via resampling of sporting events to resemble simulating seasons of performance. While the example in this chapter is based on hockey data, we make connections to other sports throughout and provide research projects with information about available resources for students to begin their own sports analytics research portfolio.

9. Using Regression Adjusted Plus-Minus to Quantify Player Effect in Team Sports

   Brian Macdonald, Nicholas Clark, Bennett Hellman, Michael Schuckers

   Abstract

   In team sports the impact of individual players on their team’s performance is an important question. Traditional summaries of a player’s performance in a game or a season have some limitations. They do not represent all actions taken by a player that can help his or her team win games, and they can be influenced by the player’s teammates, both of which limit their ability to measure the player’s true impact on a game’s outcome. Regression-based adjusted plus-minus metrics were created in part to address these concerns and have become one of the foundational classes of metrics in sports analytics. The majority of these models can be viewed as a generalized linear model (GLM), each with distinct characteristics. In this chapter, we provide a framework to understand these methods, focusing on model formulation, design structures, and choices for the response variables. We close with some open research problems that are formulated in the last section. The sample code is available for the methods described herein at https://github.com/bmacGTPM/apm-primer/tree/main/R.