INDIAN SCIENCE CONGRESS Mumbai 2015 Actuarial Science Symposium G. P. Patil Penn State University, University Park, PA USA

INSURANCE ENTERPRISE RISK MANAGEMENT CONTROL CYCLE : CERTAIN STATISICAL ISSUES AND APPROACHES Multi-Indicator Systems for Ranking, Prioritization, Detection, and Selection with Multiple Risk Measures Risk Monitoring, Data Collection, Selection Bias, and Weighted Distributions Personal Involvements with Actuarial-type Areas

Insurance ERM Control Cycle

A PUBLIC POLICY PRACTICE NOTE EXPOSURE DRAFT Insurance Enterprise Risk Management Practices March 2013 Developed by the ERM Committee of the American Academy of Actuaries The American Academy of Actuaries is a 17,000-member professional association whose mission is to serve the public and the U.S. actuarial profession. The Academy assists public policymakers on all levels by providing leadership, objective expertise, and actuarial advice on risk and financial security issues. The Academy also sets qualification, practice, and professionalism standards for actuaries in the United States.

Stochastic Modeling Involves estimating statistical distributions of potential outcomes using random variables for one or more inputs over time.. Could include ESG simulations of potential outcomes of the economies and financial markets.. The distributions of potential outcomes and extreme losses indicated by stochastic models often form the basis for computing key risk metrics/ measures of the organization.

Data requirements and risk model selections are inter-related The choice of risk models will affect data requirements. Modeling complexities and options involve data element choices. Actuaries need to understand the impact of the values of the data elements on the key risk metrics used by the organization.The impacts are implicit also on risk monitoring and risk mitigation.

Offender Actuarial Risk Assessment Actuarial risk assessment focusses on both static/ unchangeable and dynamic factors that influence recidivism ( all types of criminal offences ).. Some notable examples of actuarial scales are: Violence Risk Appraisal Guide ( VRAG ) Statistical Information on Recidivism Scale ( SIR ) Sex Offender Need Assessment Rating ( SONAR )

Multiple Actuarial Measures Different actuarial risk measures produce different risk rankings for sexual offenders Five actuarial risk instruments commonly used with adult sex offenders: RRASOR, Static99, VRAG, SORAG, MnSOST-R. Discrepancies in percentile ranks; Rank ranges vary inversely to correlations between risk measures Guidance to clinicians in resolving discrepancies between instruments based on underlying factors, such as, antisocial behavior, etc.

9 Federal Agency Partnership CDC DOD EPA NASA NIH NOAA USFS USGS Agency Databases Thematic Databases Other Databases Homeland Security Disaster Management Public Health Ecosystem Health Other Case Studies Statistical Processing: Hotspot Detection, Prioritization, etc. Data Sharing, Interoperable Middleware Standard or De Facto Data Model, Data Format, Data Access Arbitrary Data Model, Data Format, Data Access Application Specific De Facto Data/Information Standard Agency Databases Thematic Databases Other Databases Homeland Security Disaster Management Public Health Ecosystem Health Other Case Studies Statistical Processing: Hotspot Detection, Prioritization, etc. Data Sharing, Interoperable Middleware Standard or De Facto Data Model, Data Format, Data Access Arbitrary Data Model, Data Format, Data Access Application Specific De Facto Data/Information Standard SurvellanceGeoinformaticsof Hotspot Detection, Prioritization and Early Warning NSF Digital Government Project # PI: G. P. Patil Websites: NSF Digital Government surveillance geoinformatics project, federal agency partnership and national applications for digital governance. Cellular Surface National and International Applications Biosurveillance Carbon Management Coastal Management Community Infrastructure Crop Surveillance Disaster Management Disease Surveillance Ecosystem Health Environmental Justice Environmental Management Environmental Policy Homeland Security Invasive Species Poverty Policy Public Health Public Health and Environment Robotic Networks Sensor Networks Social Networks Syndromic Surveillance Tsunami Inundation Urban Crime Water Management

10 Figure 14. Rank-intervals for all 106 countries. The intervals (countries) are labeled by their midpoints as shown along the horizontal axis. For each interval, the lower endpoint and the upper endpoint are shown vertically. The length of each interval corresponds to the ambiguity inherent in attempting to rank that country among all 106 countries.

Actuarial Data Collection, Selection Bias, and Weighted Distributions Sampling individuals at random in a survey, but recording the life lengths for record. For X, exponential,with mean 1, X* has mean 2, double that of X, as a result of size bias in selection. Patil and Rao Patil, Rao, and Zelen Patil, and Taillie Patil, Rao, and Ratnaparkhi 11

recorded x is not an observation on X, but on the rv X w, say, having a pdf where ω is the normalizing factor obtained to make the total probability equal to unity by choosing ω D E[wX, ˇ]. The rv X w is called the weighted version of X, and its distribution in relation to that of X is called the weighted distribution with weight function w.