Purpose: Send an email to admin every time an exception occurs while executing business logic.
Till now I have come across \"throwing advice\" which is fine and gets
AFAIK there is no pointcut expression for this...
You should consider configuring your logger to do what you need.
Replace ae.printStackTrace(); by something like logger.warn(ae) (to print stacktraces to the console is quite bad practice anyways), and configure one of the email-sending appenders of your logging tool, e.g. log4j's or logback's SMTPAppender. Additionally, to make your configuration easier, you may use a business-dedicated logger.
If you really want to use aspects here, I think you'll have to expect all your business exceptions to bubble up at least one method, in order to use afterThrowing advices.