# References and Further Reading

## Table of Contents
1. [Foundational Papers](#foundational-papers)
2. [Books and Textbooks](#books-and-textbooks)
6. [Software and Tools](#software-and-tools)
7. [Online Resources](#online-resources)
8. [Related Frameworks](#related-frameworks)

![Tree Rings](photos/tree_rings.jpg)

(foundational-papers)=
## 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](https://doi.org/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](https://doi.org/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](https://doi.org/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](https://arxiv.org/abs/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.
- DOI: [10.1002/j.1538-7305.1956.tb03809.x](https://doi.org/10.1002/j.1538-7305.1956.tb03809.x)
- Key contribution: Original Kelly criterion formulation
- Relevance: Optimal betting/investment strategy foundation

**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](https://gwern.net/doc/statistics/decision/1975-thorp.pdf)
- 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](https://doi.org/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](https://doi.org/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)=
## 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)=
## Software and Tools

### Python Libraries

**chainladder-python**
- Website: [chainladder-python.readthedocs.io](https://chainladder-python.readthedocs.io/)
- Documentation: [chainladder-python user guide](https://chainladder-python.readthedocs.io/en/latest/user_guide/)
- Usage: Actuarial functions specializing in reserving

**Matplotlib/Seaborn**
- Matplotlib: [matplotlib.org](https://matplotlib.org/)
- Seaborn: [seaborn.pydata.org](https://seaborn.pydata.org/)
- Usage: Data visualization

**NumPy**
- Website: [numpy.org](https://numpy.org/)
- Documentation: [numpy.org/doc](https://numpy.org/doc/stable/)
- Usage: Numerical computing foundation

**Pandas**
- Website: [pandas.pydata.org](https://pandas.pydata.org/)
- Documentation: [pandas.pydata.org/docs](https://pandas.pydata.org/docs/)
- Usage: Data manipulation and analysis

**quActuary**
- Website: [quactuary.com](https://quactuary.com/)
- Documentation: [docs.quactuary.com](https://docs.quactuary.com/)
- Usage: Presently offers a strong simulation framework and an extensive library of actuarial distributions

**SciPy**
- Website: [scipy.org](https://scipy.org/)
- Documentation: [docs.scipy.org](https://docs.scipy.org/doc/scipy/)
- Usage: Scientific computing and optimization

### Actuarial Software

**Commercial Tools**
- **@RISK**: Monte Carlo simulation add-in for Excel

(online-resources)=
## Online Resources

### Educational Websites

**Casualty Actuarial Society (CAS)**
- Website: [casact.org](https://www.casact.org/)
- Resources: Property-casualty focus, research
- Relevance: Non-life insurance expertise

**London Mathematical Laboratory**
- Website: [lml.org.uk](https://lml.org.uk/)
- Resources: Ergodic economics research and tutorials

**Society of Actuaries (SOA)**
- Website: [soa.org](https://www.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](https://www.coursera.org/)

**edX**
- "Introduction to Investments" (IIMB)
- "Risk Management in Banking and Financial Institutions" (NYIF)
- Website: [edx.org](https://www.edx.org/)

### Blogs and Forums

**Ergodicity Economics**
- URL: [ergodicityeconomics.com](https://ergodicityeconomics.com/)
- Content: Blog posts on ergodic theory applications

**Quantitative Finance Stack Exchange**
- URL: [quant.stackexchange.com](https://quant.stackexchange.com/)
- Content: Q&A for quantitative finance professionals

(related-frameworks)=
## Related Frameworks

### Enterprise Risk Management

**COSO Framework**
- Organization: Committee of Sponsoring Organizations
- Website: [coso.org](https://www.coso.org/)
- Relevance: Integrated risk management framework

**ISO 31000**
- Standard: Risk management guidelines
- Organization: International Organization for Standardization
- Relevance: International risk management standard

### Regulatory Frameworks

**Solvency II**
- Region: European Union
- Focus: Insurance company solvency requirements
- Documentation: [EIOPA website](https://www.eiopa.europa.eu/)

**NAIC Risk-Based Capital**
- Region: United States
- Focus: Capital adequacy standards
- Documentation: [NAIC website](https://www.naic.org/)

## 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:**

```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