Modelling Under Risk and Uncertainty: An Introduction to Statistical, Phenomenological and Computational Methods

Exercises

There follows a list of exercises referring to the concepts developed in this chapter:

8.1 Perform sensitivity analysis of the total cost over a time period as a function of the uncertain inputs, grouping them into homogeneous subsets such as the yearly flood flows and so on.

8.2 Study the impact of sampling G'(X, d₁, d₂) = G(X, d₁) - G(X, d₂) at once instead of two successive independent samplings of G(X, d₁) and G(X, d₂) when comparing the two designs d₁ and d₂ for different types of risk measures. Discuss the pros and cons in design comparison; more generally, what about the case of optimisation over a grid {d_k}_k of competing designs?

8.3 Study the impact of modelling when switching aleatory uncertainty (independently sampled every year) into epistemic uncertainty (sampled once and constant over the time period) on the variance of the total cost over time, for instance for the Strickler friction coefficient or the economic uncertainty factor.

8.4 Study the interest of a real options approach for the flood risk problem. Considering first the risk model only, does a delayed decision to build a tall dike bring any benefit on average (or increase the risk?)? Assume then that a forecast model becomes available, taking the example of the log-autoregressive pseudo-hydrological model in Section 5.5. What should be the orders of magnitude of the times of interest and building delays, in comparison with the length of correlation, for option-taking to become beneficial?

Notes ...