In traditional projects risk is defined as the issues that may cause the project to overrun its schedule or budget in order to complete the specified functionality. Some methods, like RUP, are risk driven, meaning the highest risks should be mitigated early in the project.
In agile projects risk management is built into the process, meaning we are adaptive to all events that might influence the schedule, budget or functionality. Agile projects also focus less on being predictive and less on having fixed plans, which means they are less exposed to risks.
In agile projects we don’t have the traditional risk workshop. Instead we address risks continuously throughout the project in the iteration planning, daily stand-up meetings, retrospectives etc. All activities related to risk management end up on the backlogs ready to be prioritized together with all the other product development activities. In Scrum the product backlog is prioritized having the most customer valued features on top (not being risk driven).
Traditionally risks are handled by the project manager. However, in Scrum we sacked the project manager in favour of the Scrum master. Instead the team owns the risk management in agile projects.
Read this excellent article on risks in agile projects.
I have been working as a software consultant for more than 11 years. Because of that I am an eager supporter of lean principles and agile methods.