Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

This book provides the most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management. Whether you are a financial risk analyst, actuary, regulator or student of quantitative finance, Quantitative Risk Management gives you the practical tools you need to solve real-world problems. Describing the latest advances in the field, Quantitative Risk Management covers the methods for market, credit and operational risk modelling. It places standard industry approaches on a more formal footing and explores key concepts such as loss distributions, risk measures and risk aggregation and allocation principles. The book's methodology draws on diverse quantitative disciplines, from mathematical finance and statistics to econometrics and actuarial mathematics. A primary theme throughout is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. Proven in the classroom, the book also covers advanced topics like credit derivatives. Fully revised and expanded to reflect developments in the field since the financial crisis Features shorter chapters to facilitate teaching and learning Provides enhanced coverage of Solvency II and insurance risk management and extended treatment of credit risk, including counterparty credit risk and CDO pricing Includes a new chapter on market risk and new material on risk measures and risk aggregation

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Quantitative Risk Management: Concepts, Techniques, and Tools

Extremal events play an increasingly important role in stochastic modelling in insurance and finance. Over many years, probabilists and statisticians have developed techniques for the description, analysis and prediction of such events. In the present paper, we review the relevant theory which may also be used in the wider context of Operation Research. Various applications from the field of insurance and finance are discussed. Via an extensive list of references, the reader is guided towards further material related to the above problem areas.

https://link.springer.com/content/pdf/10.1007/BF01440733.pdf

Modelling of extremal events in insurance and finance

Preface. Part 1: Introduction. 1. Why do a risk analysis? 1.1. Moving on from "What If" Scenarios. 1.2. The Risk Analysis Process. 1.3. Risk Management Options. 1.4. Evaluating Risk Management Options. 1.5. Inefficiencies in Transferring Risks to Others. 1.6. Risk Registers. 2. Planning a risk analysis. 2.1. Questions and Motives. 2.2. Determine the Assumptions that are Acceptable or Required. 2.3. Time and Timing. 2.4. You'll Need a Good Risk Analyst or Team. 3. The quality of a risk analysis. 3.1. The Reasons Why a Risk Analysis can be Terrible. 3.2. Communicating the Quality of Data Used in a Risk Analysis. 3.3. Level of Criticality. 3.4. The Biggest Uncertainty in a Risk Analysis. 3.5. Iterate. 4. Choice of model structure. 4.1. Software Tools and the Models they Build. 4.2. Calculation Methods. 4.3. Uncertainty and Variability. 4.4. How Monte Carlo Simulation Works. 4.5. Simulation Modelling. 5. Understanding and using the results of a risk analysis. 5.1. Writing a Risk Analysis Report. 5.2. Explaining a Model's Assumptions. 5.3. Graphical Presentation of a Model's Results. 5.4. Statistical Methods of Analysing Results. Part 2: Introduction. 6. Probability mathematics and simulation. 6.1. Probability Distribution Equations. 6.2. The Definition of "Probability". 6.3. Probability Rules. 6.4. Statistical Measures. 7. Building and running a model. 7.1. Model Design and Scope. 7.2. Building Models that are Easy to Check and Modify. 7.3. Building Models that are Efficient. 7.4. Most Common Modelling Errors. 8. Some basic random processes. 8.1. Introduction. 8.2. The Binomial Process. 8.3. The Poisson Process. 8.4. The Hypergeometric Process. 8.5. Central Limit Theorem. 8.6. Renewal Processes. 8.7. Mixture Distributions. 8.8. Martingales. 8.9. Miscellaneous Example. 9. Data and statistics. 9.1. Classical Statistics. 9.2. Bayesian Inference. 9.3. The Bootstrap. 9.4. Maximum Entropy Principle. 9.5. Which Technique Should You Use? 9.6. Adding uncertainty in Simple Linear Least-Squares Regression Analysis. 10. Fitting distributions to data. 10.1. Analysing the Properties of the Observed Data. 10.2. Fitting a Non-Parametric Distribution to the Observed Data. 10.3. Fitting a First-Order Parametric Distribution to Observed Data. 10.4. Fitting a Second-Order Parametric Distribution to Observed Data. 11. Sums of random variables. 11.1. The Basic Problem. 11.2. Aggregate Distributions. 12. Forecasting with uncertainty. 12.1. The Properties of a Time Series Forecast. 12.2. Common Financial Time Series Models. 12.3. Autoregressive Models. 12.4. Markov Chain Models. 12.5. Birth and Death Models. 12.6. Time Series Projection of Events Occurring Randomly in Time. 12.7. Time Series Models with Leading Indicators. 12.8. Comparing Forecasting Fits for Different Models. 12.9. Long-Term Forecasting. 13. Modelling correlation and dependencies. 13.1. Introduction. 13.2. Rank Order Correlation. 13.3. Copulas. 13.4. The Envelope Method. 13.5. Multiple Correlation Using a Look-Up Table. 14. Eliciting from expert opinion. 14.1. Introduction. 14.2. Sources of Error in Subjective Estimation. 14.3. Modelling Techniques. 14.4. Calibrating Subject Matter Experts. 14.5. Conducting a Brainstorming Session. 14.6. Conducting the Interview. 15. Testing and modelling causal relationships. 15.1. Campylobacter Example. 15.2. Types of Model to Analyse Data. 15.3. From Risk Factors to Causes. 15.4. Evaluating Evidence. 15.5. The Limits of Causal Arguments. 15.6. An Example of a Qualitative Causal Analysis. 15.7. Is Causal Analysis Essential? 16. Optimisation in risk analysis. 16.1. Introduction. 16.2. Optimisation Methods. 16.3. Risk Analysis Modelling and Optimisation. 16.4. Working Example: Optimal Allocation of Mineral Pots. 17. Checking and validating a model. 17.1. Spreadsheet Model Errors. 17.2. Checking Model Behaviour. 17.3. Comparing Predictions Against Reality. 18. Discounted cashflow modelling. 18.1. Useful Time Series Models of Sales and Market Size. 18.2. Summing Random Variables. 18.3. Summing Variable Margins on Variable Revenues. 18.4. Financial Measures in Risk Analysis. 19. Project risk analysis. 19.1. Cost Risk Analysis. 19.2. Schedule Risk Analysis. 19.3. Portfolios of risks. 19.4. Cascading Risks. 20. Insurance and finance risk analysis modelling. 20.1. Operational Risk Modelling. 20.2. Credit Risk. 20.3. Credit Ratings and Markov Chain Models. 20.4. Other Areas of Financial Risk. 20.5. Measures of Risk. 20.6. Term Life Insurance. 20.7. Accident Insurance. 20.8. Modelling a Correlated Insurance Portfolio. 20.9. Modelling Extremes. 20.10. Premium Calculations. 21. Microbial food safety risk assessment. 21.1. Growth and Attenuation Models. 21.2. Dose-Response Models. 21.3. Is Monte Carlo Simulation the Right Approach? 21.4. Some Model Simplifications. 22. Animal import risk assessment. 22.1. Testing for an Infected Animal. 22.2. Estimating True Prevalence in a Population. 22.3. Importing Problems. 22.4. Confidence of Detecting an Infected Group. 22.5. Miscellaneous Animal Health and Food Safety Problems. I. Guide for lecturers. II. About ModelRisk. III. A compendium of distributions. III.1. Discrete and Continuous Distributions. III.2. Bounded and Unbounded Distributions. III.3. Parametric and Non-Parametric Distributions. III.4. Univariate and Multivariate Distributions. III.5. Lists of Applications and the Most Useful Distributions. III.6. How to Read Probability Distribution Equations. III.7. The Distributions. III.8. Introduction to Creating Your Own Distributions. III.9. Approximation of One Distribution with Another. III.10. Recursive Formulae for Discrete Distributions. III.11. A Visual Observation On The Behaviour Of Distributions. IV. Further reading. V. Vose Consulting. References. Index.

Risk Analysis: A Quantitative Guide

The package fitdistrplus provides functions for fitting univariate distributions to different types of data (continuous censored or non-censored data and discrete data) and allowing different estimation methods (maximum likelihood, moment matching, quantile matching and maximum goodness-of-fit estimation). Outputs of fitdist and fitdistcens functions are S3 objects, for which specific methods are provided, including summary, plot and quantile. This package also provides various functions to compare the fit of several distributions to the same data set and can handle to bootstrap parameter estimates. Detailed examples are given in food risk assessment, ecotoxicology and insurance contexts.

fitdistrplus: An R Package for Fitting Distributions

Preface. Acknowledgments. PART I: INTRODUCTION. 1. Modeling. PART II: ACTUARIAL MODELS. 2. Random Variables. 3. Basic Distributional Quantities. 4. Classifying and Creating Distributions. 5. Frequency and Severity with Coverage Modifications. 6. Aggregate Loss Models. 7. Discrete Time Ruin Models. 8. Continuous Time Ruin Models. PART III: CONSTRUCTION OF EMPIRICAL MODELS. 9. Review of Mathematical Statistics. 10. Estimation for Complete Data. 11. Estimation for Modified Data. PART IV: PARAMETRIC STATISTICAL METHODS. 12. Parameter Estimation. 13. Model Selection. 14. Five Examples. PART V: ADJUSTED ESTIMATES AND SIMULATION. 15. Interpolation and Smoothing. 16. Credibility. 17. Simulation. Appendix A: An Inventory of Continuous Distributions. Appendix B: An Inventory of Discrete Distributions. Appendix C: Frequency and Severity Relationships. Appendix D: The Recursive Formula. Appendix E: Discretization of the Serverity Distribution. Appendix F: Numerical Optimization and Solution of Systems. References. Index.

Loss Models: From Data to Decisions

Compound dlstributmns such as the compound Pmsson and the compound negative binomial are used extensively m the theory of risk to model the distributmn off the total claims incurred m a fixed period of time The usual method of evaluating the dlqtributmn functmn requires the computatmn of many convolutions of the conditional d~atnbutmn of the amount of a claim given that a clmm has occurred When the expected number of claims is large, the computatmn can become unwmldy even with modern large scale electronic computers In tlus paper, a recurs|xe definitmn of the distribution of total clmms is developed for a family of claml numbel distnbutmns and arbitrary claim amount distributions When the clam1 amount is discrete, the recursive dehnitmn can be used to compute the distribution of total claims without the use of convolutions. This can reduce the number of required computations by several orders of magnitude for sufhcmntlv large portfolios Results for some spemfic dlatnbutmna have been prevmusly obtained using generating functions and Laplace transforms (see PANJER (1980) including dlscussmn). The simple algebraic proof of this paper yields all the previous results as special case~

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Recursive Evaluation of a Family of Compound Distributions

In this paper, we take an axiomatic approach to characterize insurance prices in a competitive market setting. We present four axioms to describe the behavior of market insurance prices. From these axioms it follows that the price of an insurance risk has a Choquet integral representation with respect to a distorted probability (Yaari, 1987). We propose an additional axiom for reducing compound risks. This axiom determines that the distortion function is a power function.

Axiomatic characterization of insurance prices

Insurance risk models

Preface. Acknowledgments. PART I: INTRODUCTIN TO OPERATIONAL RISK MODELING. 1. Operational Risk. 2. Basic Probability concepts. 3. Measures of Risk. PART II: PROBABILISTIC TOOLS FOR OPERATIONAL RISK MODELING. 4. Models for the size of losses: Continuous distributions. 5. Models for the number of losses: Counting distributions. 6. Aggregate loss models. 7. Extreme value theory: The study of jumbo losses. 8. Multivariate models. PART III: STATISTICAL METHODS FOR CALIBRATING MODELS OF OPERATIONAL RISK. 9. Review of mathematical statistics. 10. Parameter Estimation. 11. Estimation for discrete distributions. 12. Model selection. 13. Fitting extreme value models. 14. Fitting copula models. Appendix A: Gamma and related functions. Appendix B: Discretization of the severity distribution. Appendix C: Nelder-Mead simplex Method. References. Index.

Harry H. Panjer

Papers

Loss Models: From Data to Decisions

Recursive Evaluation of a Family of Compound Distributions

Axiomatic characterization of insurance prices

Insurance risk models

Operational Risk : Modeling Analytics