References and Further Reading

Table of Contents

  1. Foundational Papers

  2. Books and Textbooks

  3. Software and Tools

  4. Online Resources

  5. Related Frameworks

Tree Rings

Foundational Papers

Roughly in order of recommended reading.

Ergodic Economics

Peters, O. (2019). The ergodicity problem in economics. Nature Physics, 15(12), 1216-1221.

  • DOI: 10.1038/s41567-019-0732-0

  • Key contribution: Comprehensive overview of ergodicity in economic systems

  • Relevance: Core theoretical foundation for this project

Peters, O., & Gell-Mann, M. (2016). Evaluating gambles using dynamics. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(2), 023103.

  • DOI: 10.1063/1.4940236

  • Key contribution: Time-average framework for decision-making

  • Relevance: Mathematical basis for insurance optimization

Peters, O. (2011). The time resolution of the St Petersburg paradox. Philosophical Transactions of the Royal Society A, 369(1956), 4913-4931.

  • DOI: 10.1098/rsta.2011.0065

  • Key contribution: Resolution of classical paradox using time averages

  • Relevance: Historical context and motivation

Peters, O., & Adamou, A. (2018). The evolutionary advantage of cooperation. arXiv preprint.

  • arXiv: 1506.03414

  • Key contribution: Cooperation emerges from ergodic considerations

  • Relevance: Insurance as cooperative risk-sharing

Kelly Criterion and Growth

Kelly Jr, J. L. (1956). A new interpretation of information rate. The Bell System Technical Journal, 35(4), 917-926.

Thorp, E. O. (1971). Portfolio choice and the Kelly criterion. Proceedings of the Business and Economics Section of the American Statistical Association, 215-224.

  • Gwern Branwen: Full Text

  • Key contribution: Kelly criterion applied to portfolio management

  • Relevance: Extension to multiple assets and insurance

Multiplicative Processes

Redner, S. (1990). Random multiplicative processes: An elementary tutorial. American Journal of Physics, 58(3), 267-273.

  • DOI: 10.1119/1.16497

  • Key contribution: Accessible introduction to multiplicative processes

  • Relevance: Understanding wealth dynamics

Levy, M., & Solomon, S. (1997). New evidence for the power-law distribution of wealth. Physica A, 242(1-2), 90-94.

  • DOI: 10.1016/S0378-4371(97)00217-3

  • Key contribution: Empirical evidence for multiplicative wealth dynamics

  • Relevance: Real-world validation of theoretical models

Books and Textbooks

Sections are roughly in recommended study order. Books in each section are listed chronologically by latest publication date.

Ergodicity

Peters, O., & Adamou, A. (2025). An Introduction to Ergodicity Economics. LML Press.

  • ISBN: 978-1-0686491-3-4

  • Topics: Ergodicity and implications to individuals and populations

Kelly Criterion

MacLean, L. C., Thorp, E. O., & Ziemba, W. T. (2011). The Kelly capital growth investment criterion: Theory and practice. World Scientific.

  • ISBN: 978-981-4293-53-0

  • Key contribution: Comprehensive treatment of Kelly criterion

Actuarial Science

Klugman, S. A., Panjer, H. H., & Willmot, G. E. (2019). Loss Models: From Data to Decisions. John Wiley & Sons.

  • ISBN: 978-1-119-52378-9

  • Topics: Frequency-severity models, aggregate loss distributions

Risk Management

Hull, J. C. (2018). Risk Management and Financial Institutions. John Wiley & Sons.

  • ISBN: 978-1-119-44811-2

  • Topics: Market risk, credit risk, operational risk

  • Relevance: Comprehensive risk management overview

Sweeting, P. (2017). Financial Enterprise Risk Management. Cambridge University Press.

  • ISBN: 978-1-107-18461-9

  • Topics: ERM, extreme value theory, economic capital

McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press.

  • ISBN: 978-0-691-16627-8

  • Topics: Risk measures, dependence modeling, extreme value theory

  • Relevance: Advanced risk management techniques

Statistics

Efron, B., & Hastie, T. (2021). Computer Age Statistical Inference. Cambridge University Press.

  • ISBN: 978-1-108-82341-8

  • Topics: Classical statistical methods, computationally-intense modern statistical methods

Taleb, N. N. (2020). Statistical Consequences of Fat Tails. STEM Academic Press.

  • ISBN: 978-1-5445-0805-4

  • Topics: Fat tails, metaprobability, options

Wasserman, L. (2005). All of Statistics. Springer.

  • ISBN: 0-387-40272-1

  • Probability, statistical inference, statistical models and methods

Aitchison, J., & Brown, J. A. C. (1976). The Lognormal Distribution. Cambridge University Press.

  • ISBN: 0-521-04011-6

  • Topics: Lognormal distribution monograph

Stochastic Processes

Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications.. Springer.

  • ISBN: 978-3-540-04758-2

  • Topics: Brownian motion, Itô calculus, SDEs

Ross, S. M. (2014). Introduction to Probability Models.. Academic Press.

  • ISBN: 978-0-12-407948-9

  • Topics: Markov chains, Poisson processes, queuing theory

Extreme Value Theory

Embrechts, P., Klüppelberg, C., & Mikosch, T. (2010). Modelling Extremal Events for Insurance and Finance. Springer.

  • ISBN: 978-3-540-60931-5

  • Topics: Heavy-tailed distributions, extreme value theory

de Haan, L., & Ferreira, A. (2006). Extreme Value Theory: An Introduction. Springer.

  • ISBN: 978-0-387-23946-0

  • Topics: Extreme value theory in finite- and infinite-dimensional settings

Beirlant, J., Goegebeur, Y., Segers, J., & Teugels, J. (2004). Statistics of Extremes: Theory and Applications. John Wiley & Sons.

  • ISBN: 978-0-471-97647-9

  • Topics: Statistical inference for extremes, applications

Ruin Theory

Asmussen, S., & Albrecher, H. (2010). Ruin Probabilities. World Scientific.

  • ISBN: 978-981-4282-52-9

  • Topics: Classical and modern ruin theory

Grandell, J. (1992). Aspects of Risk Theory. Springer.

  • ISBN: 978-0-387-97447-8

  • Topics: Compound Poisson processes, ruin probabilities

Optimal Control

Pham, H. (2009). Continuous-time Stochastic Control and Optimization with Financial Applications. Springer.

  • ISBN: 978-3-540-89499-5

  • Topics: Stochastic control, applications to insurance

  • Relevance: Insurance and investment optimization

Fleming, W. H., & Soner, H. M. (2006). Controlled Markov Processes and Viscosity Solutions. Springer.

  • ISBN: 978-0-387-26045-7

  • Topics: HJB equations, viscosity solutions

  • Relevance: Mathematical framework for optimal control

Portfolio Theory

Mildenhall, S. J., & Major, J. A. (2022) Pricing Insurance Risk. John Wiley & Sons.

  • ISBN: 978-1-119-75567-8

  • Risk, portfolio pricing, price allocation

Rebonato, R., & Denev, A. (2014). Portfolio Management Under Stress. Cambridge University Press

  • ISBN: 978-1-107-04811-9

  • Topics: Bayesian-net approach to coherent asset allocation

Luenberger, D. G. (2013). Investment Science. Oxford University Press.

  • ISBN: 978-0-19-974008-6

  • Topics: Portfolio optimization, asset pricing

  • Relevance: Investment theory foundations

Merton, R. C. (1992). Continuous-Time Finance. Blackwell.

  • ISBN: 978-0-631-18508-2

  • Topics: Optimal portfolio selection, consumption-investment

  • Relevance: Continuous-time optimization methods

Monte Carlo Methods

Robert, C. P., & Casella, G. (2004). Monte Carlo Statistical Methods. Springer.

  • ISBN: 978-0-387-21239-5

  • Topics: MCMC, convergence diagnostics, applications

Glasserman, P. (2003). Monte Carlo Methods in Financial Engineering. Springer.

  • ISBN: 978-0-387-00451-8

  • Topics: Variance reduction, importance sampling, quasi-Monte Carlo

Bootstrap Methods

Davison, A. C., & Hinkley, D. V. (1997). Bootstrap Methods and their Application. Cambridge University Press.

  • ISBN: 978-0-521-57391-7

  • Topics: Advanced bootstrap techniques, applications

Shao, J., & Tu, D. (1995). The Jackknife and Bootstrap. Springer.

  • ISBN: 978-0-387-94515-6

  • Jackknife, bootstrap, and other resampling methods

Efron, B., & Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman and Hall/CRC.

  • ISBN: 978-0-412-04231-7

  • Topics: Bootstrap confidence intervals, hypothesis testing

Time Series Analysis

Tsay, R. S. (2010). Analysis of Financial Time Series. John Wiley & Sons.

  • ISBN: 978-0-470-41435-4

  • Topics: GARCH models, risk management, backtesting

Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.

  • ISBN: 978-0-691-04289-3

  • Topics: State space models, filtering, forecasting

Software and Tools

Python Libraries

chainladder-python

Matplotlib/Seaborn

NumPy

Pandas

quActuary

  • Website: quactuary.com

  • Documentation: docs.quactuary.com

  • Usage: Presently offers a strong simulation framework and an extensive library of actuarial distributions

SciPy

Actuarial Software

Commercial Tools

  • @RISK: Monte Carlo simulation add-in for Excel

Online Resources

Educational Websites

Casualty Actuarial Society (CAS)

  • Website: casact.org

  • Resources: Property-casualty focus, research

  • Relevance: Non-life insurance expertise

London Mathematical Laboratory

  • Website: lml.org.uk

  • Resources: Ergodic economics research and tutorials

Society of Actuaries (SOA)

  • Website: soa.org

  • Resources: Research papers, educational materials

  • Relevance: Professional actuarial resources

Online Courses

Coursera

  • “Financial Engineering and Risk Management” (Columbia University)

  • “Introduction to Actuarial Science” (University of Pennsylvania)

  • Website: coursera.org

edX

  • “Introduction to Investments” (IIMB)

  • “Risk Management in Banking and Financial Institutions” (NYIF)

  • Website: edx.org

Blogs and Forums

Ergodicity Economics

Quantitative Finance Stack Exchange

Implementation Examples

Jupyter Notebooks

Ergodic Insurance Optimization

  • Current project notebooks in /notebooks/ directory

  • Topics: Manufacturer simulation, optimization, validation

  • Language: Python

Citation Guidelines

How to Cite This Work

APA Format:


Filiakov, A. (2025). Ergodic Insurance Limits: Optimizing insurance using time-average growth [Software]. GitHub.
    https://ergodicityadvantage.com

BibTeX:

@software{ergodicinsurancelimits,
  author = {Filiakov, Alex},
  title = {Ergodic Insurance Limits: Optimizing insurance using time-average growth},
  year = {2025},
  publisher = {GitHub},
  url = {https://ergodicityadvantage.com}
}

Acknowledgments

This project builds upon the foundational work of Ole Peters and the London Mathematical Laboratory in developing ergodic economics. I also acknowledge the contributions of the actuarial and quantitative finance communities in developing the mathematical tools and frameworks used in this implementation.

Updates and Corrections

For updates to this reference list or to suggest additional resources, please:

  1. Open an issue on GitHub

  2. Submit a pull request with additions

  3. Contact the maintainers

Last updated: September 2025 Version: 0.3.0

Verification Note

All references have been verified as of September 2025. Some resources may change over time. For the most current information:

  • Check DOI links for academic papers

  • Visit organization websites directly

  • Search GitHub for latest community implementations

  • Consult academic databases for recent publications