Library
Excel Model for Power Transform Tail Factors
Ledger has developed a novel tail factor model that generalizes several other well-known tail factor models in the actuarial literature. The attached Excel file allows for practitioners to fit this ta...
Blurry Images and Hierarchical Models
We share a series of blurry images and ask you, the reader, to make some predictions about those pictures. We then use this series of examples to illustrate the power and value of ...
Line of Business Volume and Diversification
The US property & casualty industry is subdivided into 22 separate lines of business in Schedule P of the annual statements mandated by the NAIC. We explore the relative size of ea...
Line of Business Development Patterns
When an insurance company issues a policy, the company knows the amount of premium it will receive, but it may not know for many years exactly how much it will cost to settle all o...
Line of Business Loss Ratio Behavior
The core measure of an insurance company's performance is its loss ratio. We describe what loss ratios are, and how they tend to behave. We explore how loss ratios vary by line of ...
Ledger's Loss Forecasting Strategy
Ledger uses a strategy for forecasting casualty insurance loss ratios that is significantly different from traditional actuarial practice. We describe how Ledger's analytics team a...
Blurry Images and Hierarchical Models
We share a series of blurry images and ask you, the reader, to make some predictions about those pictures. We then use this series of examples to illustrate the power and value of ...
Loss Ratio Dynamics
We rely on time series models for estimating the loss ratios insurers will achieve in future years. Our choice of models is not arbitrary or purely driven by backtesting performanc...
Loss Ratio Volatility and Insurer Skill
Many investors are interested in understanding just how volatile insurer loss ratios are, and how much of that volatility is intrinsic to the insurance environment. We present a to...
Ledger's Modeling Philosophy
Ledger Investing does not use actuarial science to price risk. We explain why we don't, and provide an intuitive justification of our alternate method through an analogy to a fund ...
Casualty Insurance Lines of Business
Property & casualty insurance includes a wide number of distinct insurance products with widely varying characteristics. We describe what, fundamentally, property & casualty insura...
Property & Casualty Insurance Companies
We look at basic features of insurance companies by exploring statutory filings data. We see how many property & casualty insurance companies there are, and how insurance groups ar...
Ledger's Modeling Philosophy
Ledger Investing does not use actuarial science to price risk. We explain why we don't, and provide an intuitive justification of our alternate method through an analogy to a fund ...
Prior Distributions for Link Ratios
Many traditional loss development models center around the notion of link ratios. We describe the importance of prior distributions in the context of Bayesian modeling, and some of...
Loss Ratio Volatility and Insurer Skill
Many investors are interested in understanding just how volatile insurer loss ratios are, and how much of that volatility is intrinsic to the insurance environment. We present a to...
Loss Ratio Dynamics
We rely on time series models for estimating the loss ratios insurers will achieve in future years. Our choice of models is not arbitrary or purely driven by backtesting performanc...
Property and Casualty Insurance Industry Analysis
This anthology is a collection of articles we've written on the property and casualty insurance industry. It covers basics of the property and casualty insurance space, analyses of...
A Bayesian workflow for securitizing casualty insurance risk
In this paper, we lay out our Bayesian workflow for securitizing casualty insurance-linked securities that uses: (1) theoretically informed time-series and state-space models to ca...
Joint estimation of insurance loss development factors using Bayesian hidden Markov models
Loss development modeling is typically conducted in two steps: one model to estimate the link ratios (age-to-age factors or loss development factors) from the main portion of the t...
Improved Estimation of Parametric Tail Factor Models
Loss development tail factors are difficult to estimate, due to training data that is typically quite sparse and volatile. We propose a new estimation technique that is well-grounde...
A Power Transform Generalization of Parametric Tail Factor Methods
Many tail factor estimation methods in common usage revolve around fitting a parametric curve to age-to-age factors or link ratios. In this paper, we propose a new parametric curve...
BayesBlend: Easy Model Blending using Pseudo-Bayesian Model Averaging and Stacking in Python
Averaging predictions from multiple candidate inferential models frequently outperforms predictions from any given candidate model in isolation. Here, we introduce BayesBlend, the ...