A benchmark approach to quantitative finance

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In recent years, financial derivatives have become essential tools for risk managers and investors, with insurance products now integral to both personal and business portfolios. The management of mutual and pension funds has gained significance for individuals, while banks, insurance companies, and corporations increasingly utilize financial and insurance instruments for active risk management. A wider range of securities allows for tailored hedging strategies to meet the specific needs of various investors and companies. Mastering modern quantitative methods is crucial for distinguishing market participants in finance and insurance. Consequently, financial institutions, insurance firms, and corporations must develop expertise in quantitative finance, where many associated methods and technologies originate. This book serves as an introduction to quantitative finance, focusing on the mathematical framework used in financial modeling, derivative pricing, portfolio selection, and risk management. It presents a unified approach to risk and performance management through the benchmark approach, which differs from the prevailing paradigm. This systematic and rigorous method employs the growth optimal portfolio as numeraire and the real-world probability measure as the pricing measure.