Go to project Dashboard for which you want to see the executions
Click on Test Executions tab
On test executions list page click on Assigned to me
This will shortlist the Test Executions that have been assigned to you.
All options remain same as they are on Test Executions' list page, except for the fact that the list is limited to the tests that have been assigned to you enabling you to focus on those Test Executions and perform relevant operations including opting to execute them.