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Since the groundbreaking work of Nobel Laureates Markowitz, Black, Scholes and Merton, mathematics has emerged as the leading discipline to address fundamental questions in finance. After the success of the pricing theories in the early nineties, risk management is attracting a great deal of attention in the academic community, triggering its increasing protagonism in the banking as well as in the insurance and utility industry. This book provides an accessible and practical introduction to the basic elements of financial risk management, mathematics and computational finance for both students and traders. Too often students learn techniques and analyses without assessing the dependence of such analyses on the definition of 'uncertainty' and the meaning of 'probability.' Likewise many traders use the mathematical and computational techniques without understanding the underlying theory. Thus this book attempts to clarify some of the issues confronting theory and practice and explain some of the 'fundamental-mathematical' issues that underpin the theory of finance.