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1209 results in Optimization, OR and risk

Page 1 of 61

Markov Decision Processes and Reinforcement Learning
  • Martin L. Puterman, Timothy C. Y. Chan
  • Coming soon
  • Expected online publication date:
    June 2026
    Print publication:
    30 June 2026
  • This book offers a comprehensive introduction to Markov decision process and reinforcement learning fundamentals using common mathematical notation and language. Its goal is to provide a solid foundation that enables readers to engage meaningfully with these rapidly evolving fields. Topics covered include finite and infinite horizon models, partially observable models, value function approximation, simulation-based methods, Monte Carlo methods, and Q-learning. Rigorous mathematical concepts and algorithmic developments are supported by numerous worked examples. As an up-to-date successor to Martin L. Puterman's influential 1994 textbook, this volume assumes familiarity with probability, mathematical notation, and proof techniques. It is ideally suited for students, researchers, and professionals in operations research, computer science, engineering, and economics.

Risk Measures
  • An Introduction to the Mathematical Theory
  • Ilya Molchanov, Johanna Ziegel
  • Published online:
    26 February 2026
    Print publication:
    19 February 2026
  • Providing comprehensive yet accessible coverage, this is the first graduate-level textbook dedicated to the mathematical theory of risk measures. It explains how economic and financial principles result in a profound mathematical theory that allows us to quantify risk in monetary terms, giving rise to risk measures. Each chapter is designed to match the length of one or two lectures, covering the core theory in a self-contained manner, with exercises included in every chapter. Additional material sections then provide further background and insights for those looking to delve deeper. This two-layer modular design makes the book suitable as the basis for diverse lecture courses of varying length and level, and a valuable resource for researchers.

  • Introduction

  • Ilya Molchanov, Universität Bern, Switzerland, Johanna Ziegel, ETH Zürich
  • Book:
    Risk Measures
    Published online:
    26 February 2026
    Print publication:
    19 February 2026, pp ix-xi
    • Chapter
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  • Summary

    This chapter provides a systematic introduction to the book.

  • 1 - Gains, Quantiles, and Value-at-Risk

  • Ilya Molchanov, Universität Bern, Switzerland, Johanna Ziegel, ETH Zürich
  • Book:
    Risk Measures
    Published online:
    26 February 2026
    Print publication:
    19 February 2026, pp 1-14

  • Summary

    This chapter introduces financial risk as a random variable representing uncertain future gains or losses. A risk measure quantifies this uncertainty by mapping random variables to real numbers. The prominent example of Value-at-Risk (V@R) is discussed.

  • 4 - Average-Value-at-Risk

  • Ilya Molchanov, Universität Bern, Switzerland, Johanna Ziegel, ETH Zürich
  • Book:
    Risk Measures
    Published online:
    26 February 2026
    Print publication:
    19 February 2026, pp 43-54

  • Summary

    The Average-Value-at-Risk (AV@R) has emerged as a superior, coherent risk measure that accounts for the magnitude of potential losses beyond a given quantile and consistently favors diversification.

  • 12 - Multivariate Risk Measures

  • Ilya Molchanov, Universität Bern, Switzerland, Johanna Ziegel, ETH Zürich
  • Book:
    Risk Measures
    Published online:
    26 February 2026
    Print publication:
    19 February 2026, pp 165-184

  • Summary

    This chapter presents the main ideas behind measuring the risks of random vectors. The main point is that it may be possible to transfer assets between components of a vector, and so the risk measure becomes a convex set in Euclidean space.

Page 1 of 61