In Outlook

go to File >> Options >> Mail

On the right hand side  in the " Send Messages" section

uncheck " Delete Meeting requests and notifications from Inbox after responding"

Outlook 2013 and Outlook 2010 crash shortly after start when you have an iCloud Internet Calendar added to your Outlook profile.
 

This is a known issue and both Apple and Microsoft are working on it.

http://support.microsoft.com/kb/3019219?wa=wsignin1.0

https://discussions.apple.com/thread/6663515?start=30&tstart=0

Which is all well and good , but what do you do in the mean time.

Here is a simple work around. You need a Google account.

Sign in to Google calendar , Add the Icalendar

Other Calendar >> Add by URL and paste or type in the Icalendar URL.

The go to settings in the gear icon in top right. Next click on Calendars and click on the Icalendar you just added.

Towards the bottom of the page the Calendar address will be displayed. you have three options XML , ICAL and HTML.

Use this ICAL address in Outlook and it will work.