Bibliography

Aas, Kjersti, Claudia Czado, Arnoldo Frigessi, and Henrik Bakken. 2009. Pair-copula constructions of multiple dependence.” Insurance: Mathematics and Economics 44 (2): 182–98. https://doi.org/10.1016/j.insmatheco.2007.02.001.
Actuarial Standards Board. 2007. Property/Casualty Unpaid Claim Estimates.” Actuarial Standard of Practice No. 43.
Actuarial Standards Board. 2011. Treatment of Profit and Contingency Provisions and the Cost of Capital in Property / Casualty Insurance Ratemaking.” Actuarial Standard of Practice No. 30.
Actuarial Standards Board. 2019. Modeling.” Actuarial Standard of Practice No. 56, no. 56.
Artzner, Philippe, Freddy Delbaen, Jean-Marc Eber, and David Heath. 1999. Coherent measures of risk.” Mathematical Finance 9 (3): 203–28. http://onlinelibrary.wiley.com/doi/10.1111/1467-9965.00068/abstract.
Blanchard III, Ralph S. 2008. Basic Insurance Accounting – Selected Topics. July. CAS Study Note.
Bodoff, Neil M. 2007. Capital Allocation by Percentile Layer.” Variance 3 (1): 13–30.
Bolstad, William M, and James M Curran. 2016. Introduction to Bayesian Statistics. John Wiley & Sons.
Brehm, Paul J, Spencer M Gluck, Kreps Rodney E, et al. 2007. “Enterprise Risk Analysis for Property & Liability Insurance Companies.” Guy Carpenter & Company, LLC.
Bühlmann, Hans. 1985. Premium Calculation from Top Down.” ASTIN Bulletin 15 (2): 89–101. https://doi.org/10.2143/ast.15.2.2015021.
Caramagno, Nicholas, David Mamane, and Liam Neilson. 2021. An Introduction to IFRS 17 for P&C Actuaries. Casualty Actuarial Society. https://www.ifrs.org/issued-standards/list-of-standards/ifrs-17-insurance-contracts/.
Casualty Actuarial Society. 2022. Complete Text References for Exam 7, Syllabus of Basic Education. https://www.casact.org/sites/default/files/2021-03/7_individual_textref.pdf.
Chan, Cynthia et al. 2024. Insurance Rating Criteria. Fitch Ratings. https://www.fitchratings.com/research/insurance/insurance-rating-criteria-04-03-2024.
Cherny, Alexander, and Dilip Madan. 2009. New measures for performance evaluation.” Review of Financial Studies 22 (7): 2571–606. https://doi.org/10.1093/rfs/hhn081.
Conning. 2020. “A User’s Guide to Economic Scenario Generation in Property/Casualty Insurance.” CAS Research Papers. https://www.casact.org/sites/default/files/2021-02/economic-scenario-generation-conning1020.pdf.
Cont, Rama, Romain Deguest, and Giacomo Scandolo. 2010. Robustness and sensitivity analysis of risk measurement procedures.” Quantitative Finance 10 (6): 593–606. https://doi.org/10.1080/14697681003685597.
Cummins, J. David. 1990. Multi-Period Discounted Cash Flow Rate-making Models in Property-Liability Insurance.” Journal of Risk and Insurance 57 (1): 79–109.
Cummins, J. David. 2000. Allocation of capital in the insurance industry.” Risk Management and Insurance Review, nos. October 1998: 7–28. http://onlinelibrary.wiley.com/doi/10.1111/j.1540-6296.2000.tb00013.x/full.
Daykin, Chris D, Teivo Pentikainen, and Martti Pesonen. 1993. Practical Risk Theory for Actuaries. Chapman; Hall/CRC.
Delbaen, Freddy. 2000. Coherent Risk Measusres.” Blätter Der DGVFM 10 (24(4)): 733–39. https://doi.org/10.1007/BF02808276.
EIOPA. 2009. Directive 138/2009/EC (Solvency II Directive). European Insurance and Occupational Pension Authority. https://www.eiopa.europa.eu/rulebook/solvency-ii-single-rulebook/directive-1382009ec-solvency-ii-directive_en.
EIOPA. 2015. Delegated Regulation (EU) 2015/35. European Insurance and Occupational Pension Authority. https://www.eiopa.europa.eu/rulebook/solvency-ii-single-rulebook/delegated-regulation-eu-201535_en.
Eling, Martin, and David Holzmüller. 2008. An Overview and Comparison of Risk-Based Capital Standards.” Journal of Insurance Regulation 26 (4): 31–60.
Embrechts, Paul. 2010. Risk Aggregation presentation.” Copula Theory and Its Applications, 111–26. https://doi.org/10.1007/978-3-642-12465-5.
Emma, Charles C et al. 2000. Dynamic Financial Models of Property-Casualty Insurers. Casualty Actuarial Society. https://www.casact.org/sites/default/files/database/forum_00wforum_00wf317.pdf.
Fairley, William B. 1979. Investment Income and Profit Margins in Property-Liability Insurance: Theory and Empirical Results.” The Bell Journal of Economics 10 (1): 192. https://doi.org/10.2307/3003326.
Floreani, Alberto. 2011. Risk margin estimation through the cost of capital approach: Some conceptual issues.” Geneva Papers on Risk and Insurance: Issues and Practice 36 (2): 226–53. https://doi.org/10.1057/gpp.2011.2.
Friedland, Jacqueline. 2010. “Estimating Unpaid Claims Using Basic Techniques.” https://www.casact.org/sites/default/files/database/studynotes_friedland_estimating.pdf.
Friedman, J, T Hastie, and R Tibshirani. 2008. The elements of statistical learning. Second. Springer. http://www-stat.stanford.edu/$\sim$tibs/book/preface.ps.
Gabaix, Xavier, and David I Laibson. 2008. The Seven Properties of Good Models. https://dash.harvard.edu/bitstream/handle/1/4481492/laibson_sevenproperties.pdf?sequence=2.
Geisser, Seymour. 2017. Predictive Inference. Chapman; Hall/CRC.
Golub, Gene H, and Charles F Van Loan. 2013. Matrix Computations. Johns Hopkins University Press.
Hansen, Lars Peter, and Thomas J Sargent. 2008. Robustness. https://doi.org/10.1007/978-1-4471-5562-1_7.
Heynderickx, W., J. Cariboni, W. Schoutens, and B. Smits. 2016. The relationship between risk-neutral and actual default probabilities: the credit risk premium.” Applied Economics 48 (42): 4066–81. https://doi.org/10.1080/00036846.2016.1150953.
IAA Risk Margin Working Group. 2009. Measurement of Liabilities for Insurance Contracts: Current Estimates and Risk Margins. International Actuarial Assocation.
IAIS. 2008. Standard on the Use of Internal Models for Regulatory Capital Purposes. no. July. https://www.iaisweb.org/uploads/2022/01/16__Standard_No__2_2_7_on_the_use_of_Internal_Models_for_regulatory_capiital_purposes.pdf.
Jakobsen, Mathilde, Timothy Prince, Brad Herman, and Mahesh Mistry. 2020. Understanding Universal BCAR. A. M. Best.
Jewson, Stephen, Trevor Sweeting, and Lynne Jewson. 2025. Reducing reliability bias in assessments of extreme weather risk using calibrating priors.” Advances in Statistical Climatology, Meteorology and Oceanography 11 (1): 1–22. https://doi.org/10.5194/ascmo-11-1-2025.
Jouini, E., W. Schachermayer, and N. Touzi. 2008. Optimal risk sharing for law invariant monetary utility functions.” Mathematical Finance 18 (2): 269–92. https://doi.org/10.1111/j.1467-9965.2007.00332.x.
Karakuyu, Ali, Mark Button, et al. 2023. Criteria | Insurance | General: Insurer Risk-Based Capital Adequacy–Methodology and Assumptions. https://www.spglobal.com/ratings/en/about/criteria/insurance-rbc-criteria-2023.
Klugman, Stuart A, Harry H Panjer, and Gordon E Willmot. 2019. Loss Models: From Data to Decisions. 5th ed. Vol. 715. John Wiley & Sons.
Koca, Stephen et al. 2023. Statements of Actuarial Opinion on Property and Casualty Loss Reserves. American Academy of Actuaries. https://www.actuary.org/sites/default/files/2023-12/casualty-practice-note-saopclossreserves.pdf.
Koenker, Roger, and Kevin F Hallock. 2001. “Quantile Regression.” Journal of Economic Perspectives 15 (4): 143–56. https://www.aeaweb.org/articles?id=10.1257/jep.15.4.143.
Kovvali, Narayan. 2022. Theory and Applications of Gaussian Quadrature Methods. Springer Nature.
Kozik, Thomas J. 1994. Underwriting betas-the shadows of ghosts.” Proceedings of the Casualty Actuarial Society 81 (154, 155): 303–29.
Kreps, Rodney E. 1997. Parameter Uncertainty in (Log)normal Distributions. https://www.casact.org/sites/default/files/database/proceed_proceed97_97553.pdf.
Major, John A. 1999. Taking Uncertainty Into Account: Bias Issues Arising from Parameter Uncertainty in Risk Models.” CAS Forum Summer (153-196).
Major, John A., Ruodu Wang, and Micah G. Woolstenhulme. 2015. The Most Dangerous Model: A Natural Benchmark for Assessing Model Risk.” Society of Actuaries Monograph: Enterprise Risk Management Symposium, 1–45.
McClenahan, Charles L. 1999. Insurance Profitability.” Actuarial Considerations Regarding Risk and Return, 113–24.
McNeil, Alexander J, Paul Embrechts, and Rudiger Frey. 2005. Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press. https://doi.org/10.1198/jasa.2006.s156.
Meyers, Glenn G. 2019. Stochastic Loss Reserving Using Bayesian MCMC Models. Second. CAS Monograph Series.
Mildenhall, Stephen J. 2004. A Note on the Myers and Read Capital Allocation Formula.” North American Actuarial Journal 8 (2): 32–44. http://library.soa.org/library-pdf/naaj0402_3.pdf.
Mildenhall, Stephen J. 2017. In Praise of Value at Risk.” Actuarial Review 44(6): 48–50. https://ar.casact.org/in-praise-of-value-at-risk/.
Mildenhall, Stephen J. 2022. When is Premium Riskier Than Loss? https://www.convexrisk.com/static/talks/MILDENHALL_When_Is_Premium_Riskier_Than_Loss_2022.pdf.
Mildenhall, Stephen J. 2023a. Aggregate Software Documentation. https://aggregate.readthedocs.io/en/latest/.
Mildenhall, Stephen J. 2023b. aggregate: Frequency-Severity Distributions Made Easy.” Actuarial Review 50(3): 31–34. https://ar.casact.org/aggregate-frequency-severity-distributions-made-easy/.
Mildenhall, Stephen J. 2024. Aggregate: fast, accurate, and flexible approximation of compound probability distributions.” Annals of Actuarial Science, 1–40. https://doi.org/10.1017/S1748499524000216.
Mildenhall, Stephen J. 2005. Correlation and Aggregate Loss Distributions With An Emphasis On The Iman-Conover Method.” Casualty Actuarial Society Forum Winter. https://www.casact.org/sites/default/files/database/forum_06wforum_06w107.pdf.
Mildenhall, Stephen J, and John A Major. 2022. Pricing Insurance Risk: Theory and Practice. John Wiley & Sons, Inc.
Myers, Stewart C, and Richard A Cohn. 1987. A discounted cash flow approach to property-liability insurance rate regulation.” In Fair Rate of Return in Property-Liability Insurance. Springer.
NAIC. 2024. Risk-Based Capital. https://content.naic.org/insurance-topics/risk-based-capital.
Odomirok, Kathleen C, Liam M Mcfarlane, Gareth L Kennedy, and Justin J Brenden. 2020. Casualty Actuarial Society Financial Reporting through the Lens of a Property/Casualty Actuary. Casualty Actuarial Society.
Postek, Krzysztof, Alessandro Zocca, Joaquim Gromicho, and Jeffrey Kantor. 2024a. “Companion Jupyter Book for “Hands-On Mathematical Optimization with Python’’.” Https://mobook.github.io/MO-book/intro.html; GitHub.
Postek, Krzysztof, Alessandro Zocca, Joaquim Gromicho, and Jeffrey Kantor. 2024b. Hands-On Mathematical Optimization with Python. Cambridge University Press.
Press, William H., Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. 1992. Numerical Recipes in C. 2nd Editio. Cambridge University Press.
Reitano, Robert R. 1997. Two paradigms for the market value of liabilities.” North American Actuarial Journal 1 (4): 104–22. https://doi.org/10.1080/10920277.1997.10595657.
Robbin, Ira. 1992. The Underwriting Profit Provision. Casualty Actuarial Society Study Note.
Smith, Ralph C. 2024. Uncertainty Quantification: Theory, Implementation, and Applications. SIAM.
Society of Actuaries. 2024. Economic Scenario Generators|SOA. https://www.soa.org/resources/tables-calcs-tools/research-scenario/.
Szkoda, Susan T et al. 1995. CAS Dynamic Financial Analysis Property/Casualty Insurance Companies Handbook. Casualty Actuarial Society. https://www.casact.org/sites/default/files/database/forum_96wforum_96wf001.pdf.
Tasche, Dirk. 1999. Risk contributions and performance measurement.” Report of the Lehrstuhl Fur Mathematische Statistik, TU Munchen, 1–26. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.68.9393&rep=rep1&type=pdf.
Venter, Gary G. 1991. Premium Calculation Implications of Reinsurance Without Arbitrage.” ASTIN Bulletin 21 (02): 223–30. https://doi.org/10.2143/ast.21.2.2005365.
Venter, Gary G., John A. Major, and Rodney E. Kreps. 2006. Marginal Decomposition of Risk Measures.” ASTIN Bulletin 36 (2): 375–413. https://doi.org/10.2143/AST.36.2.2017927.
Wand, Matt P, and M Chris Jones. 1994. Kernel Smoothing. CRC press. http://matt-wand.utsacademics.info/webWJbook/KernelSmoothingSample.pdf.
Wang, Shaun S. 1996. Premium Calculation by Transforming the Layer Premium Density.” ASTIN Bulletin 26 (01): 71–92. https://doi.org/10.2143/AST.26.1.563234.
Wang, Shaun S. 1998. Aggregation of correlated risk portfolios: models and algorithms.” Proceedings of the Casualty Actuarial Society, 848–939. http://www.casact.com/pubs/proceed/proceed98/980848.pdf.
Wang, Shaun S. 2000. A class of distorion operators for pricing financial and insurance risks.” Journal of Risk and Insurance 67 (1): 15–36.
Wuthrich, Mario V., and Michael Merz. 2015. Stochastic Claims Reserving Manual: Advances in Dynamic Modeling.
Wüthrich, Mario V, Hans Bühlmann, Hansjörg Furrer, et al. 2010. Market-Consistent Actuarial Valuation. Vol. 2. Springer.