The course provides the basic elements of risk and decision analysis. It will cover case studies, methods and tools currently used in the domain. A key aspect is on how to deal with random variables. It is indispensable to obtain the most accurate values for the probabilities of the outcomes, as well as for the costs of failure. It is important to define precisely the correlations, or links between the variables. An additional issue is on how to decide under uncertainties. For instance, considering the worst case cannot work in general, since it will lead to negative decisions in many situations. This raises the issue of accepting some risks to get opportunities. The general idea is to mitigate risks as much as possible, and to be prepared to handle situations when risks materialize. Risk and Decision Analysis is a combination of quantitative techniques, organizational aspects as well as behavioural considerations.  
General Course Information  
Risk analysis is prevalent in most technical and business aspects of economic activity. The 2008 financial crisis transformed into a general economic and industrial meltdown shows that the key issue in business and government decisions lies in the understanding and mitigation of risks. On the other hand risks are the counterpart of opportunities. Without taking risks there is no human activity. More globally the situation is that of decision making under uncertainty.
The general idea is to replace the variables of interest by random variables (or time dependent random variables termed as "stochastic processes"). How to decide in front of random variables? A first difficulty is to get the right probability distributions. The outcome is not unique, so it is indispensable to obtain the most accurate values of the probabilities of these outcomes. 
A second difficulty lies in the correlations, or links between the variables. In a deterministic framework, if a link exists, it is clear and explicit. One variable is a function of another one. In a probabilistic set up this is not apparent. It may have catastrophic consequences. In a physical system like a building, one may have extremely reliable elements and a high risk of collapse. The globalization which is at the origin of the 2008 crisis is a good example of the consequences of links. No activity is immune, because links are not apparent. 
A third difficulty is on how to decide in front of probabilities. Consider an investment decision; if the framework is deterministic, the decision is easy. One simply compares the discounted cash flow to the investment cost. Clearly it is far from obvious in a probabilistic framework. The solution does not lie either in the worst case scenario. In general this leads to a negative decision. This emphasizes that 0- risk is not possible in a meaningful world.  
Course Description  
In this course, one will review the techniques which exist to deal with uncertainties in decision making. From basic situations in which a simple risk-consequence analysis can be performed, to more complex situations in which one manipulates random variables, a progressive approach will be performed. The course is self-contained. All what is necessary to know in probability and statistics will be presented, but of course it is helpful to have some background.  
The course will review in particular the techniques to improve the knowledge on probability distributions with learning procedures, how to derive solid information from expert opinion, the differences between structural randomness and uncertainties. 
The interaction between risk management and systems engineering and management will be described and illustrated. Techniques of decision making under uncertainties, like utility functions, risk indicators (value at risk) will be presented.  
One will also insist on the fact that techniques do not eliminate risks, but allow integrating them in the decision process.