Research Trends and Opportunities in Actuarial Science and Financial Mathematics

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Research Trends and Opportunitiesin Actuarial
Science andFinancial 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

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Actuarial Science andFinancial
MathematicsDoing Integrals forFun and Profit
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Presentation Agenda

• Actuaries who (or what) are they?
• Actuarial exams and subject matter
• Recent developments in
• Actuarial practice
• Academic research

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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

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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

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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

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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

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Basic Actuarial Exams

• Exam P Probability
• Exam FM Financial mathematics
• Exam MLC Life contingencies
• Exam MFE Financial economics
• Exam C Actuarial modeling

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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

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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!
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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

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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

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The Actuarial ScienceResearch Triangle
Mathematics
Fuzzy Set Theory
Stochastic Calculus / Itos Lemma
Theory of Risk
Markov Chain Monte Carlo
Interest Theory
Financial Mathematics
Credibility Theory
Chaos and Complexity
Dynamic Financial Analysis
Interest Rate Modeling
Actuarial Science
Finance
Portfolio Theory
Contingent Claims Analysis
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Actuarial Science and Finance

• Coaching is not rocket science.
• - Theresa Grentz, former University of Illinois
  Womens 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.

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Actuarial Science and Finance (cont.)

• Actuarial science and finance are not rocket
  science theyre harder
• Rocket science
• Test a theory or design
• Learn and re-test until successful
• Actuarial science and finance
• Things continually change behaviors,
  attitudes,.
• Cant hold other variables constant
• Limited data with which to test theories

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Research a sample ofActuarial Journals

• North American Actuarial Journal (SoA)
• Variance (CAS)
• Scandinavian Actuarial Journal
• ASTIN Bulletin
• Insurance Mathematics and Economics

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Research Interests AmongCasualty Actuaries

• Stochastic modeling
• Predictive modeling
• Generating economic and financial scenarios
• Modeling operational risk
• Quantifying and modeling systemic risk

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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

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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

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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

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ResearchOther 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

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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

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gorvett_at_illinois.edu
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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/