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Working Papers |
| A Multivariate
Bayesian Claim Count Development Model With Closed Form Posterior
and Predictive Distributions, January 2005 Abstract: This paper presents a rich, yet tractable, multivariate Bayesian model of claim count development. The model combines two conjugate families: the gamma-Poisson distribution for ultimate claim counts and the Dirichlet-multinomial distribution for emergence. We compute closed form expressions for all distributions of actuarial interest, including the posterior distribution of parameters and the predictive multivariate distribution of future counts given observed counts to date and for each of these distributions give a closed form expression for the moments. A new feature of the model is its explicit sensitivity to ultimate claim count variability and the uncertainty surrounding claim count emergence. Depending on the value of these parameters, the posterior mean can equal the BF or chain-ladder reserve. Thus the model provides a continuum of models interpolating between these common methods. We give an example to illustrate use of the model. |
| Correlation and Aggregate Loss Distributions With An Emphasis on the Iman Conover Method CAS Correlation Working Party, July 2005 |
Publications |
| Discussion of Generalized Minimum Bias Models, CAS Ratemaking Discussion Papers, 2005 |
| The Bailey-Simon Method, Wiley Encyclopedia of Actuarial Science, 2004 |
| A Note on the Myers and Read Capital Allocation Formula, NAAJ April 2004 |
| Revised Discussion of Myers-Read with Further Examples CAS Forum (Discussion of 2002 ARIA Prize Paper), Fall 2003 |
| Application of the Option Pricing Paradigm to the Solution of Insurance Problems by Michael Wacek, Discussion by Mildenhall, Proceedings of the Casualty Actuarial Society, 2000 |
| A systematic relationship between minimum bias and generalized linear models Proceedings of the Casualty Actuarial Society, 1999 |
| Cycles in a Product of Modular Curves and a Group Analogous to the Class Group, Duke Math Journal, 1992 |
Talks and Presentations |
| Integration & Aggregation in Risk Management: An Insurance Perspective CAS Spring Meeting, May 2005 |
| The Iman-Conover Method CAS Spring Meeting, May 2004 |
| Risk Premium for Insurance Product Pricing CAS/SOA ERM Symposium, July 2003 |
| Discussion of Myers-Read CAS Spring Meeting, May 2003 (Example Spreadsheet) |
| Finance and Insurance: Converging or Diverging? Talk to Howard Bolnick's Kellogg MBA Class, May 2003 |
| The Intersection of Finance and Insurance Midwestern Actuarial Forum, March 2003 |
| The Evolution of Property-Casualty Insurance Liabilities Seminar on Industrial Problems, Institute for Mathematics and its Applications, Minnesota MN, January 2003 |
| COTOR Shareware Software Proposal COTOR committee meeting at CAS Spring Meeting, San Diego CA, May 2002 |
| Finance and Insurance: Converging or Diverging? Talk to Howard Bolnick's Kellogg MBA Class, May 2002 |
| Actuarial Applications of the FFT to Computing Aggregate Loss Distribution September 2001, Computational Finance Seminar, Purdue University |
| Practical Issues in Computing Aggregate Loss Distributions July 2001 CARe, Washington DC |
| Computing with Bivariate Distributions July 2001 ASTIN, Washington DC |
| The Intersection of Finance and Insurance Talk to Howard Bolnick's Kellogg MBA Class, May 2001 |
| Actuarial Methods and Reinsurance Company Results (Exhibits) Purdue Actuarial Club, October 2000 |
| Property Casualty Insurance Talk to Karl Cowan's class at Purdue University, October 2000 |
| The Intersection of Finance and Insurance Talk to Howard Bolnick's Kellogg MBA Class, May 2000 |
| Recent Developments in Transferring Risk CAS Spring Meeting, Las Vegas, May 2000 |
| Applications of the Option Pricing Paradigm to Insurance (Discussion) CAS Spring Meeting, Las Vegas, May 2000 |
| What are the Actuarials? A Guide to Correct Usage April 2000, CNA Re Training Seminar (jokes only) |
| Bayesian-Bootstrap Loss Development July 1999 DFA, Chicago IL |
| The Role of Reinsurance in a Total Risk Management Program (with John Beckman) CAS CARe Seminar Baltimore MD, June 1999 |
| Four Actuarial Applications of the Bootstrap AIB Bootstrap Workshop, May 1999 |
| A Systematic Relationship Between Minimum Bias and Generarlized Linear Models CAS Spring Meeting, Orlando Fl, May 1999 |
| Liability Dynamics CAS DFA Seminar, Boston MA, July 1998 |
| Pricing and Use of Aggregate Distributions CARe Practicioner's Track, Standford CT, June 1998 |
| Convergence and Its Impact on Actuaries CNA Actuarial Seminar, June 1998 |
| Black Scholes Lunch Bunch Seminar at CNA Re, September 1997 |
| Wang's Proportional Hazard Transform Lunch Bunch Seminar at CNA Re, August 1997 |
Other Miscellany |
| How to discount cumulative losses without computing incremental losses |
| Notes on Frequency Distributions September 1999 |
| Solutions to an Option Pricing Problem September 1998 |
| Finance Bibliography July 1997 |
| Modeling Loss Ratios May 1997 |
| MATLAB routine to compute distribution of length of a game of shutes and ladders |
| Premium Margins and Managing Catastrophe Risk, 1995 |
| Solution to the ABRACADABRA problem |
| A Note on Elkies Proof 1991 |
| (c) 2002 Stephen Mildenhall Updated Jan 2, 2004 |