Algorithms for Worst-Case Design and Applications to Risk Management
Risk management topics are treated in this book in a way that is different from what the reader might think of first. World-wide experience during the last decade shows, that it is perhaps more realistic to consider worst possible scenarios in the financial world than just to perform inference based on more optimistic criteria. The roots of the presented ideas and methods arise in part from the theory of games, in particular from the minimax principle. This seems to be the leitmotif. The title of the book does not really describe the content of the book and may be misleading. There is much more in the book than just algorithms. Most of the key concepts of financial mathematics are clearly explained and discussed in the text. Nevertheless, the fundamental idea of “worst-case” is thoroughly kept through the whole text. Let us describe just a sample from a broad area of topics covered in the book’s eleven chapters: computing of saddle points, numerical experiments with minimax algorithms, strategies for securities’ hedging, simulation studies, asset allocation problems, asset-liability management including immunization, and currency management. In the bonanza of books on mathematical finance and/or financial mathematics, the book under review is surely an exception. The presented ideas may be exploited both in theory and practice. Strongly recommended to anyone with interest in financial mathematics and keen to acquire non-standard pieces of knowledge of standard and other financial problems. The book is also recommended to practitioners.