Risk analysis and Optimization analysis?

Can anyone please explain the concepts of risk analysis and optimization analysis? And give a brief example of both? Thanks for any sort of help that anyone can give, god bless, everyone :)

Risk analysis is a methodology for understanding the statistical likelyhood of negative events taking place. It's used extensively in the insurance and investment industries and by government emergency management.

FEMA example:
http://home.pacific.net.sg/~thk/risk.html

Optimization analysis is a branch of Decision Analysis for mathematically verifying that a decision is the optimal choice.

http://en.wikipedia.org/wiki/Optimal_decision