If you are running OSPF inside your network and already have the ASA inside interface participating in OSPF, I do not see any issues in advertizing your DMZ networks downstrean into your OSPF domain, if you do you may want to use OSPF message-digest-key MD5 in your ospf process for security authentication.
 my personal opinion is I would advertize the DMZ, otherwise you will need to statically adverize your DMZ networks but since you have a dynamic routing protocol in place use it.
If we use OSPF(advertised from the ASA), which instance should advertise the DMZ?
Usually in your ospf process number you have assign for the inside interface, advertize your DMZ with a network statement .
Im glad I could share my opinion. Just wanted to reinstate to use message-digest-key ospf authentication between your firewall and any downstream or upstream routers participating in OSPF, this way you will have additional security with OSPF and establishing secure adjacency within your firewall Parameter and routers.
Table of ContentsIntroductionVersion HistoryPossible Future
UpdatesDocuments PurposeNAT Operation in ASA 8.3+ SectionsRule Types
Network Object NATTwice NAT / Manual NATRule Types used per SectionNAT
Types used with Twice NAT / Manual NAT and Network Obje...
Table of Contents Introduction:This document describes details on how
NAT-T works. Background: ESP encrypts all critical information,
encapsulating the entire inner TCP/UDP datagram within an ESP header.
ESP is an IP protocol in the same sense that TCP an...