Stochastic Orders and Dependence
Comparing Risks in Insurance, Finance and Economics
Contents
- Preface
- List of Figures
- List of Tables
- 1Comparing Risks: Utilities, Generators and the Map of Orders
- 2The Usual, Hazard Rate and Likelihood Ratio Orders
- 3The Convex Order and Strassen’s Theorem
- 4Variability, the Lorenz Order and Majorization
- 5Multivariate Stochastic Orders
- 6Copulas, Comonotonicity and the Bounds of Dependence
- 7Dependence Orders: Supermodular, Concordance and Directionally Convex
- 8Sums of Dependent Risks and Worst-Case Bounds
- 9Insurance: Premiums, Optimal Reinsurance and Ruin
- 10Risk Measures that Respect the Orders
- 11Finance: Option Prices, Volatility and Diversification
- 12Economics: Increasing Risk, Decisions and Inequality
- References
- Index
- About the Author
About this book
Two risks with the same mean and the same variance can still be different risks. When is one risk worse than another, not for one decision maker, but for every decision maker in a whole class at once? A stochastic order answers it, and its comparisons are theorems that hold in every model.
This book proves the theory and puts it to work. It builds the usual, hazard rate, likelihood ratio, convex, stop-loss, dispersive and Lorenz orders; Strassen’s theorem; copulas, comonotonicity and the orders of dependence; and the worst cases a sum of dependent risks can reach. It then applies them to insurance premiums and optimal reinsurance, ruin, risk measures, option prices and diversification, increasing risk and the measurement of inequality.
Every main result is proved. Every chapter sets out its algorithms step by step and works them by hand.
Ilze Strautiņa is a professor of actuarial mathematics from Riga who priced reinsurance treaties for years before turning to research, and who names the order before she says “riskier”.
The covers
