* $566 bln stock market opened for applications on Monday * Tom Shippey sees cautious, long-term growth * Initial licences to number around a dozen - bankers By Simon Jessop and David French LONDON/DUBAI, June 1 (Reuters) - Emerging markets-focused investment firm Ashmore Group expects to lodge an application to invest directly in the Saudi Arabian stock market by the end of this week, its finance director told Reuters. The Gulf Arab kingdom began accepting applications from institutional investors on Monday for a licence to trade stocks on the $566 billion market, the first time foreigners will be allowed to own shares directly.