It is possible by use of Widgets. Please try the widgets in JIRA. If you want to automate this, then you can possibly write a small ReST client that will fetch the data based on a saved filter and mail it. But before you go for it, make sure to check the Marketplace for a plugin that does this.
For this case you can try the "Single Level Group By Report". The filter can be a saved filter for "All non closed issues" and the "Statistic Type" can be "Assignee". This give a neatly consolidate report of pending issues per user.
To get this report, navigate to the project that you want, go to reports and select "Single Level Group By Report.
Use the PDF View Plugin! It does exactly what you look for.
Here is a sample export composed of JIRA chart gadgets:
Davor, this should be doable with our add-on
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