Research Trends and Opportunities in Actuarial Science and Financial Mathematics Rick Gorvett, FCAS, ASA, CERA, MAAA, ARM, FRM, Ph.D. Director, Actuarial Science Program State Farm Companies Foundation Scholar in Actuarial Science University of Illinois at Urbana-Champaign MAA - Illinois North Central College April 2011

“Actuarial Science and Financial Mathematics: Doing Integrals for Fun 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 in Actuarial 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 Science Research Triangle Mathematics Actuarial Science Finance Stochastic Calculus / Ito’s Lemma Financial Mathematics Portfolio Theory Contingent Claims Analysis Fuzzy Set Theory Markov Chain Monte Carlo Chaos and Complexity Credibility Theory Dynamic Financial Analysis Interest Rate Modeling Interest Theory of 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 of Actuarial Journals North American Actuarial Journal (SoA) Variance (CAS) Scandinavian Actuarial Journal ASTIN Bulletin Insurance: Mathematics and Economics

Research Interests Among Casualty 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

Some Useful Web Pages Mine – Casualty Actuarial Society – Society of Actuaries – “Be An Actuary” –