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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: – Associates: – Total: 3,053 1,505 4,558 • Society of Actuaries: – Fellows: – Associates: – Total: 12,223 8,015 20,238 Casualty Actuaries • • • • • • • • • Insurance companies: Reinsurers: Consultants: Organizations serving insurance: Government: Brokers and agents: Academic: Other: Retired: 2,108 522 815 142 86 145 18 407 315 “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 Fuzzy Set Theory Markov Chain Monte Carlo Chaos and Complexity Actuarial Science Stochastic Calculus / Ito’s Lemma Theory of Risk Credibility Theory Dynamic Financial Analysis Portfolio Theory Interest Theory Interest Rate Modeling Contingent Claims Analysis Financial Mathematics Finance 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 actuarialor 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 [email protected] 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/