Most decision making processes involve risk associated with the uncertainty of a range of outcomes that may, or may not, occur at some time in the future. In recent years, many of the recent advances in risk theory have come from the field of financial mathematics. While the latter subject is now well developed I claim that there are still some important aspects of decision-making involving risk that are not covered by the existing theory. In particular, I believe that the following three questions require further investigations. 1. How to make big returns with high probability? 2. How to price financial derivatives on weather sensitive assets? 3. How to minimize risks associated with extreme temperatures? I proposed a number of techniques to hedge risk both in financial portfolios and in environmental problems. Hence this book supplies, at least partial, answers to each of these challenging questions. The analysis should help shed some light on this dynamic and risky financial environment, and should be especially useful to professionals in financial service, risk management in investment banking system and the energy markets.