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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/