Research Trends and Opportunitiesin Actuarial Science andFinancial Mathematics

Rick Gorvett, FCAS, ASA, CERA, MAAA, ARM, FRM, Ph.D.

Director, Actuarial Science ProgramState Farm Companies Foundation Scholar in Actuarial Science

University of Illinois at Urbana-Champaign

MAA - IllinoisNorth Central College

April 2011

“Actuarial Science andFinancial Mathematics:

Doing Integrals forFun and Profit”

Presentation Agenda

• Actuaries – who (or what) are they?

• Actuarial exams and subject matter

• Recent developments in– Actuarial practice

– Academic research

What is an Actuary?The Technical Definition

• Someone with an actuarial designation• Property / Casualty:

– FCAS: Fellow of the Casualty Actuarial Society– ACAS: Associate of the Casualty Actuarial Society

• Life:– FSA: Fellow of the Society of Actuaries– ASA: Associate of the Society of Actuaries

• Other:– EA: Enrolled Actuary– MAAA: Member, American Academy of Actuaries

What is an Actuary?Better Definitions

• “One who analyzes the current financial implications of future contingent events”

- p.1, Foundations of Casualty Actuarial Science

• “Actuaries put a price tag on future risks. They have been called financial architects and social mathematicians, because their unique combination of analytical and business skills is helping to solve a growing variety of financial and social problems.”

- p.1, Actuaries Make a Difference

Membership Statistics

• Casualty Actuarial Society:– Fellows: 3,053– Associates: 1,505– Total: 4,558

• Society of Actuaries:– Fellows: 12,223– Associates: 8,015– Total: 20,238

Casualty Actuaries

• Insurance companies: 2,108• Reinsurers: 522• Consultants: 815• Organizations serving insurance: 142• Government: 86• Brokers and agents: 145• Academic: 18• Other: 407• Retired: 315

“Basic” Actuarial Exams

• Exam P: Probability

• Exam FM: Financial mathematics

• Exam MLC: Life contingencies

• Exam MFE: Financial economics

• Exam C: Actuarial modeling

CAS Exams – Advanced Topics

• Insurance policies and coverages• Ratemaking• Loss reserving• Actuarial standards• Insurance accounting• Reinsurance• Insurance law and regulation• Finance and solvency• Investments and financial analysis

Financial Mathematics

• Advanced work in this area usually includes the following courses:– Partial differential equations– Probability theory– Numerical methods– Stochastic calculus– Computer science– Portfolio theory– Option pricing theory– Financial risk management

I wanna be a

“Quant”!

Actuarial Practice

• Types of actuaries– Life– Pension– Property & casualty

• Primary functions involve the financial implications of contingent events– Price insurance policies (“ratemaking”)– Set reserves (liabilities) for the future costs of

current obligations (“loss reserving”)– Financial analyses

Recent Developments inActuarial Practice

• Risk and return– Pricing insurance policies to formally reflect risk– Identification of effective rate classifications

• Insurance securitization– Transfer of insurance risks to the capital markets

by transforming insurance cash flows into tradable financial securities

• Dynamic financial analysis (DFA) & enterprise risk management (ERM)– Holistic approach to modeling the interaction

between insurance and financial operations

The Actuarial ScienceResearch Triangle

Mathematics

ActuarialScience

Finance

Stochastic Calculus /Ito’s Lemma

Financial Mathematics

PortfolioTheory

ContingentClaims

Analysis

Fuzzy SetTheory

Markov ChainMonte Carlo

Chaos andComplexity

CredibilityTheory

DynamicFinancialAnalysis

InterestRate

Modeling

InterestTheory

Theoryof Risk

Actuarial Science and Finance

• “Coaching is not rocket science.”

- Theresa Grentz, former University of Illinois Women’s Basketball Coach

• Are actuarial science and financial mathematics “rocket science”?

• Certainly, lots of quantitative Ph.D.s are on Wall Street and doing actuarial-

or finance-related work• But….

Actuarial Science and Finance (cont.)

• Actuarial science and finance are not rocket science – they’re harder

• Rocket science:– Test a theory or design– Learn and re-test until successful

• Actuarial science and finance– Things continually change – behaviors, attitudes,….– Can’t hold other variables constant– Limited data with which to test theories

Research: a sample ofActuarial Journals

• North American Actuarial Journal (SoA)

• Variance (CAS)

• Scandinavian Actuarial Journal

• ASTIN Bulletin

• Insurance: Mathematics and Economics

Research Interests AmongCasualty Actuaries

• Stochastic modeling

• Predictive modeling

• Generating economic and financial scenarios

• Modeling operational risk

• Quantifying and modeling systemic risk

2007 REU (“Stochastic Modeling”) Research Projects

• “A Model for Increasing Black Life Expectancy by Reducing Infant Mortality, Homicide, and HIV”

• “A Markov Chain Approach to Modeling Cancer Risk”

• “A Regime-Switching Model for Foreign Exchange Rates”

• “On the Statistical Properties of Interest Rates and a Basic Regime-Switching Model”

• “Stochastic Modeling for Illinois Prepaid Tuition Contracts”

• “A Fractal-Geometric Approach to Risk Management and Mitigation”

2009 REU (“Stochastic Modeling”) Research Projects

• Regime-switching reliability model

• Continuous-state versus discrete-state Markov chains in finance and economics

• Risk measures applied to simulated financial portfolios

• Dynamics of the unemployment process

• An “event study” of foreign exchange rates

U/G Research Associate Projects

• Neuroeconomics / cognitive biases

• Power laws

• Predator-prey models

• Agent-based models

• Fuzzy modeling of risk

• Housing wealth: reverse mortgages and equity releases

• Public pensions: securitizing pension claims

Research:Other Recent Areas

• Stochastic processes

• Economic and financial modeling

• Dynamic financial analysis

• Enterprise risk management

• Fuzzy set theory and fuzzy random variables

• Neural networks

• Data mining

• Chaos and complexity theory

Conclusion

• A new actuarial science “paradigm” is evolving– Advanced mathematics– Financial sophistication

• There are significant opportunities for important research in these areas of convergence between actuarial science, finance, and mathematics

gorvett@illinois.edu

Some Useful Web Pages

• Mine– http://www.math.uiuc.edu/~gorvett/

• Casualty Actuarial Society– http://www.casact.org/

• Society of Actuaries– http://www.soa.org/

• “Be An Actuary”– http://www.beanactuary.org/