Statistics in Insurance Business Giorgio Alfredo Spedicato Ph.D FCAS FSA C.Stat

Intro Insurance is the business of risk. It exchanges a fixed compensation (premium) against uncertain costs (benefits), in terms of timing and amounts. Insurance professionals must master probability. Actuaries are the professionals who quantifies and prices financial risks. They tell the insurance body: how much policyholder should pay (premiums). How much it should be set aside to cover existing and prospective obligations (reserves). How much economic capital it should set aside to cover unexpected downside risks (risk management).

Becoming an actuary Italy (similar to continental Europe): need to hold a degree in Statistics and / or Finance. Need to pass one comprehensive State Exam («esame di stato»). UK, US, Australia, China, India: Actuarial professional bodies define a number of specialized exams. Preliminary exams: probability, math, statistics and finance; specialty exams depend by specialization (P&C, Life, Health, Pensions). Everywhere is a regulated profession. Strong professional ethic and discipline apply. Continuous professional development needed

Classical Actuarial Works: General Insurance Products designing / pricing for coverages like: motor insurance, homeowners insurance, commercial insurance. Need to define ratings plan according to risk characteristics. Need to forecast trends in frequency and severity. Calculate reserves: How much of received premiums is «earned»? How much the insurer should set aside to pay occurred but not paid claims? Calculate Economic Capital (Solvency II)

Life Insurance Pricing of Individual and Group Products: Term and Whole life insurances. Investment products: term and unit linked products. Individual annuities. Calculate reserves Calculate economic capital

Health Insurance and Pension Funds Pricing for individual (Accident, Sickness, LTC) Group Insurance. Also defines rules for contribution and benefits for public (INPS and other Compulsory Funds) and II level pension funds. Reserving and Capital

Reinsurance & CAT Modeling Reinsurers insure Insurance Companies. Reinsurance actuaries deals with low frequency high severity risk. Often, they have to price «unique risk». Actuaries needs to deal with engineers and natural scientist to price covers for Catastrophes (Earthquakes, Hurricanes, …) risks.

Non traditional roles Banking: credit risk analytics on retail and corporate markets. Bets and Lottery: «calculate tickets» price, reward and compensation scheme. Business analytics: customer relationship management, anti -fraud.

All you need is statistics and … Actuaries price risks (SOA slogan is «risk is opportunity»). So they need a probabilistic thinking. Excellent knowledge of probability is the foundation for all statistics and insurance operations. Exam P/1 is the first exam for US actuaries (SOA and CAS)

… business judgment Micro – economic thinking is fundamental: market behaviour, competition, consumer behaviours. Macro – Economic knowledge is needed when drawing hypothesis on trends. Business knowledge, team working, soft skills are obviously assumed since the actuary is not a «lab creature», but need to provide practical and business effective solutions.

Statistical tools: probability Pure Premium is Frequency * Severity. Risk margin is often defined using percentiles. Need to know how to estimate and work with distribution moments. Capital is often defined as a percentile (VaR approach) of the NPV distribution. Distribution modeling (fitting methods, Goodness of Fit approaches) could be useful

Simulation Capital models often are hard to be solved analytically Monte Carlo approach is oftenly used. Actuaries must be familiar in using such methods.

Predictive Modeling Predictive modeling is needed for risks classification. Es: MTPL frequency and severity depend by age, gender, car, location, previous insurance claims…Policyholder retention and conversion depends by many variables Survival models needed for life insurance. Typical predictive models are: GLMs (Poisson, Gamma log linear models). Logistic regression. New data mining approaches: tree based models, random forest, ensemble models.

Big data techniques Need to know how to access and manage large data bases. Parallelization approaches, Hadoop & Spark NoSql database for network analysis