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  Risk management

Risk is a result of uncertainty, and uncertainty is the result of our limited knowledge and understanding of how and why various phenomena and events have occurred, currently occur, and will occur. Fortunately, however, taking calculated risks often results in higher potential rewards; this is most definitely the case in finance. The key word is "calculated" risk, as opposed to any risk. While we should not expect to be compensated, on average, for taking any risk, we might expect higher average returns for risks well measured and managed; this return comes as a reward for making the effort to correctly quantify and control risk.

Risk management is concerned with reducing the risk relative to the reward it is expected to produce and with avoiding the exposure to unnecessary risks. Risk management is not about eliminating all risks, as such an action is likely to eliminate all expected rewards and make a worthy enterprise worthless.

The latest developments in quantitative finance provide us with a variety of tools to manage risks. Those developments include the concept of Value-at-Risk; the variety of financial and non-financial derivative securities; the techniques of analyzing real options; as well as a variety of popular risk-management techniques, to include Monte-Carlo simulations, bootstrapping, stress-testing, etc. We focus on three types of quantitative risk management: market risk, credit risk, and operational risk.