Is it possible to exclude running the managed package test classes and only run my own org's test classes at the time of deployment using ant script?
runAllTests parameter is your friend. Look at the DeployOptions in the metadata API documentation. It states that:
If true, all Apex tests defined in the organization are run. For deployment to a production organization, all tests, except for those that originate from installed managed packages, are automatically run regardless of this argument. If any of the tests fail when the rollbackOnError parameter is set to true, the entire deployment will roll back.
So, if you simply specify runAllTests = false in your deploy call, managed package classes are automatically excluded and all your unmanaged classes are executed. If you are not migrating to a production Org, you can even turn unmanaged classes execution off but it is not possible for a production Org deploy.
Hope this helps.