Modeling the “Pseudodeductible” in Insurance Claims Decisions

References

• Antoniak C. E. Mixtures of Dirichlet processes with applications to nonparametric problems. Ann. Statist. (1974) 2(4):1152–1174Crossref, Google Scholar
• Berger P. D., Nasr N. I. Customer lifetime value: Marketing models and applications. J. Interactive Marketing (1998) 12(1):17–30Crossref, Google Scholar
• Bernardo J. M., Smith A. F. M.Bayesian Theory (2000) 2nd ed.(John Wiley and Sons, Chichester, UK) Google Scholar
• Bureau of Labor Statistics Consumer price index. (2004) . Retrieved September 23, 2004, http://www.bls.gov/cpi, series ID cuur0200sa0, cuus0200sa0Google Scholar
• Choi J. J., Laibson D., Madrian B. C. $100 bills on the sidewalk: Violations of no-arbitrage in 401-k accounts. (2005) . Working Paper 11554, NBER, Cambridge, MAGoogle Scholar
• Congdon P.Bayesian Statistical Modelling (2001) (Wiley Series in Probability and Statistics, John Wiley and Sons, Chichester, UK) Google Scholar
• De Leve G., Weeda P. J. Driving with Markov-programming. ASTIN Bull. (1968) 5(1):62–86Crossref, Google Scholar
• de Pril N. Optimal claim decisions for a bonus-malus system: A continuous approach. ASTIN Bull. (1979) 10:215–222Crossref, Google Scholar
• Dellaert N. P., Frenk J. B. G., van Rijsoort L. P. Optimal claim behavior for vehicle damage insurances. Insurance: Math. Econom. (1993) 12(3):225–244Crossref, Google Scholar
• Draper D. Discussion on “Bayesian Nonparametric Inference for Random Distributions and Related Functions.”. J. Roy. Statist. Soc., Ser. B (1999) 61(3):510–513Google Scholar
• Escobar M. D., West M. Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. (1995) 90(430):577–588Crossref, Google Scholar
• Fader P. S., Hardie B. G. S. A note on modelling underreported Poisson counts. J. Appl. Statist. (2000) 27(8):953–964Crossref, Google Scholar
• Fader P. S., Hardie B. G. S. Customer-base valuation in a contractual setting: The perils of ignoring heterogeneity. (2006) . Working paper, The Wharton School, University of Pennsylvania, Philadelphia, PAGoogle Scholar
• Ferguson T. S., Rizvi H., Rustagi J. Bayesian density estimation by mixtures of normal distributions. Recent Advances in Statistics (1983) (Academic Press, New York) 287–302Crossref, Google Scholar
• Gelman A., Meng X.-L., Stern H. Posterior predictive assessment of model fitness via realized discrepancies. Statist. Sinica (1996) 6(4):733–807Google Scholar
• Gelman A., Carlin J. B., Stern H. S., Rubin D. B.Bayesian Data Analysis (2004) (Chapman and Hall, Boca Raton, FL) Google Scholar
• Geweke J. F., Bernardo J. M., Berger J. O., Dawid A. P., Smith A. F. M. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. Bayesian Statistics (1992) Vol. 4(Oxford University Press, Oxford) 169–194Google Scholar
• Gupta S., Lehmann D. R., Stuart J. A. Valuing customers. J. Marketing Res. (2004) 41(1):7–18Crossref, Google Scholar
• Haehling von Lanzenauer C. Optimal claim decisions by policyholders in automobile insurance with merit-rating structures. Oper. Res. (1974) 22(5):979–990Link, Google Scholar
• Hardie B. G. S., Fader P. S. Applied probability models with applications in marketing. (2005) . Unpublished manuscriptGoogle Scholar
• Hastings N. A. J. Optimal claiming on vehicle insurance. Oper. Res. Quart. (1976) 27(4):805–813Crossref, Google Scholar
• Israel M. Do we drive more safely when accidents are more expensive? Identifying moral hazard from experience rating schemes. (2004) . Working paper, Northwestern University, Evanston, ILGoogle Scholar
• Johnson N. L., Kotz S., Balakrishnan N.Continuous Univariate Distributions (1994) Vol. 1(John Wiley and Sons, New York) Google Scholar
• Kahneman D., Tversky A. Prospect theory: An analysis of decision under risk. Econometrica (1979) 47(2):263–291Crossref, Google Scholar
• Kahneman D., Tversky A. Choices, values and frames. Amer. Psychologist (1984) 39(4):341–350Crossref, Google Scholar
• Kim J. G., Menzefricke U., Feinberg F. M. Assessing heterogeneity in discrete choice models using a Dirichlet process prior. Rev. Marketing Sci. (2004) 2(1):1–39Crossref, Google Scholar
• Klugman S. A., Panjer H. H., Willmot G. E.Loss Models: From Data to Decisions (1998) (John Wiley and Sons, New York) Google Scholar
• Kulkarni V. G.Modeling and Analysis of Stochastic Systems (1995) (Chapman and Hall, London, UK) Google Scholar
• Lemaire J.Bonus-Malus Systems in Automobile Insurance (1995) (Kluwer Academic Publishers, Dordrecht, The Netherlands) Crossref, Google Scholar
• Moe W. W., Fader P. S. Capturing evolving visit behavior in clickstream data. J. Interactive Marketing (2004a) 18(1):5–19Crossref, Google Scholar
• Moe W. W., Fader P. S. Dynamic conversion at e-commerce sites. Management Sci. (2004b) 50(3):326–335Link, Google Scholar
• Moffitt Robert. An economic model of welfare stigma. Amer. Econom. Rev. (1983) 73(5):1023–1035Google Scholar
• Newhouse J. P., Rolph J. E., Mori B., Murphy M. The effect of deductibles on the demand for medical care services. J. Amer. Statist. Assoc. (1980) 75(371):525–533Crossref, Google Scholar
• Newton M. A., Raftery A. E. Approximate Bayesian inference with the weighted likelihood bootstrap. J. Roy. Statist. Soc., Ser. B (1994) 56(1):3–48Google Scholar
• Norman J. M., Shearn D. C. S. Optimal claiming on vehicle insurance revisited. J. Oper. Res. Soc. (1980) 31(2):181–186Crossref, Google Scholar
• Rubin D. B. Bayesianly justifiable and relevant frequency calculations for the applied statistician. Ann. Statist. (1984) 12(4):1151–1172Crossref, Google Scholar
• Schmittlein D. C., Bemmaor A. C., Morrison D. G. Why does the NBD model work? Robustness in representing product purchases, brand purchases and imperfectly recorded purchases. Marketing Sci. (1985) 4(3):255–266Link, Google Scholar
• Sethuraman J. A constructive definition of Dirichlet priors. Statist. Sinica (1994) 4(2):639–650Google Scholar
• Spiegelhalter D. J., Thomas A., Best N. G., Gilks W. R. BUGS: Bayesian inference using Gibbs sampling. (1996) . Computer software, version 1.4. Retrieved 2004, http://www.mrc-bsu.cam.ac.uk/bugs/Google Scholar
• Stephens M. Dealing with label switching in mixture models. J. Roy. Statist. Soc., Ser. B (2000) 62(4):795–809Crossref, Google Scholar
• Thaler R. H. Toward a positive theory of consumer choice. J. Econom. Behav. Organ. (1980) 1(1):39–60Crossref, Google Scholar
• van Praag B. M. S., Vermeulen E. M. A count-amount model with endogenous recording of observations. J. Appl. Econometrics (1993) 8(4):383–395Crossref, Google Scholar
• Venezia I. Aspects of optimal automobile insurance. J. Risk Insurance (1984) 51(1):63–79Crossref, Google Scholar
• Venezia I., Levy H. Optimal claims in automobile insurance. Rev. Econom. Stud. (1980) 47(3):539–549Crossref, Google Scholar
• Walker S. G., Damien P., Laud P. W., Smith A. F. M. Bayesian nonparametric inference for random distributions and related functions. J. Roy. Statist. Soc., Ser. B (1999) 61(3):485–527Crossref, Google Scholar