http://the-iland.net/static/downloads/TransactionsAsProofOfStake.pdf
Pages 5 and 6 seem to address these issues. Also, I suspect that there's a maximum on coin day accumulation. When the inactivity fee is charged, doesn't this effectively reset the coin age to 0?
Yes it does.
Thanks for the clarification and this does eliminate the risk quite a lot.
What if I carefully choose time when large CDD just happened which means my percentage of CDD grows relatively? Also consider the diversity of shares, even if you find my attack in short time, it will be difficult to collect enough coin days to beat my alternative chain in time. It turns worse as time goes on when this alternative chain grows as I'm in the longest chain and all the following transactions are protecting me.
I think the point here is that comparing with total CDD in a block, I don't need much percentage of shares to make an attack. I suspect one block will destroy less than 1% of coin days in average. This means the cost of an attack is low. If I have 10% shares, even if it's defeated to discarded branch chain, it's relatively easy to roll back several blocks and make it survive 1 or 2 future blocks. To defeat it, you may need manual processes. This will not happen in POW if you own 10% power and it will be quite impossible that you can roll back 1 block because to do so, you'll need to win at least 2 sequencial blocks and it contains randomness. But with POS, you'll be assured your attack can work as I don't see any randomness in POS mining. Maybe we should inject some randomness in the mining to solve this issue.