Statistical Decision Problems presents a quick and concise introduction into the theory of risk, deviation and error measures that play a key role in statistical decision problems. It introduces state-of-the-art practical decision making through twenty-one case studies from real-life applications. The case studies cover a broad area of topics and the authors include links with source code and data, a very helpful tool for the reader. In its core, the text demonstrates how to use different factors to formulate statistical decision problems arising in various risk management applications, such as optimal hedging, portfolio optimization, cash flow matching, classification, and more.

The presentation is organized into three parts: selected concepts of statistical decision theory, statistical decision problems, and case studies with portfolio safeguard. The text is primarily aimed at practitioners in the areas of risk management, decision making, and statistics. However, the inclusion of a fair bit of mathematical rigor renders this monograph an excellent introduction to the theory of general error, deviation, and risk measures for graduate students. It can be used as supplementary reading for graduate courses including statistical analysis, data mining, stochastic programming, financial engineering, to name a few. The high level of detail may serve useful to applied mathematicians, engineers, and statisticians interested in modeling and managing risk in various applications.

Presents a quick and concise introduction into the theory of risk, deviation and error measures that play a key role in statistical decision problems Discusses basic principles of statistical decision making from optimization perspective in various risk management applications such as optimal hedging, portfolio optimization, portfolio replication, and more Introduces state-of-the-art practical decision making through seventeen case studies from real-life applications?

Inhalt

1. Random Variables.- 2. Deviation, Risk, and Error Measures.- 3. Probabilistic Inequalities.- 4. Maximum Likelihood Method.- 5. Entropy Maximization.- 6. Regression Models.- 7. Classification.- 8. Statistical Decision Models with Risk and Deviation.- 9. Portfolio Safeguard Case Studies.- Index.- References.