Alexander Melnikov Livres

Explores "the epic battle over a mathematical concept that shook the old order and shaped the world as we know it. On August 10, 1632, five leaders of the Society of Jesus convened in a somber Roman palazzo to pass judgment on a simple idea: that a continuous line is composed of distinct and limitlessly tiny parts. The doctrine would become the foundation of calculus, but on that fateful day the judges ruled that it was forbidden. With the stroke of a pen they set off a war for the soul of the modern world"--

The updated edition delves into the core concepts and techniques of financial mathematics, emphasizing quantitative financial analysis and the management of insurance risks. It highlights the interconnections between insurance and financial risks, offering more examples and problems. Notably, it expands on the foundations of probability and stochastic analysis, while introducing new topics such as stochastic volatility in financial markets, risk measures, risk-adjusted performance measures, and equity-linked insurance.

Focusing on stochastic analysis, this book explores its applications in mathematical finance and the statistics of random processes. It aims to present contemporary methods and results in a concise, self-contained manner, making it suitable as a textbook for senior undergraduate and graduate courses. Designed for students, instructors, and specialists, it serves as a comprehensive resource for understanding stochastic analysis and its practical implications in various fields.