Bitshares DPoS is based on a design which resembles in many ways the Raft protocol which has been through peer review in academic papers.

The Bitshares team arrived at a similar design because great minds think alike and because Bitshares developers discovered that you can do consensus through delegation of authority. Analyze and compare the Raft protocol to DPoS.

Additionally if you want to go further you can analyze LMAX architecture. When you do that you'll see that Bitshares wasn't thrown together by amateurs and that it has a rigorously academically tested (as well as tested in practice) architecture. No one has hacked DPoS 1.0, and while DPoS 2.0 is still in testing, there is no reason to believe DPoS 1.0 was ever insecure. It's security is based on the fact that in order to break consensus you have to get a critical threshold of delegates to collude without being discovered that they are colluding by the voting token holders.

Many people like to claim that Delegated Proof of Stake or Proof of Stake in general is vulnerable to theoretical black swan attacks. Bitcoin is also vulnerable to theoretical black swan attacks. The focus of our attention should be on practical attacks which have either happened in the past frequently, and which would have catastrophic consequences if pulled off. In the case of Bitshares which has been audited and which has existed for over a year, there isn't an attack which could occur frequently and which has catastrophic consequences.
 
Example1:


Example 2:

The threat level on a risk matrix is measured by the frequency of the occurrence and the amount of damage the community would suffer if it occurs. For example if a bug is found to allow hackers to remotely empty everyone's wallet this would be an example of catastrophic damage, but how often has that occurred in Proof of Stake? Double spending also would cause catastrophic damage but how often has that occurred? If it is a real treat in practice then you'll be able to provide some example cases to show that these theoretical attacks have happened.

We know in practice that centralized exchanges are extremely high risk as measured on a risk matrix. This is because these attack frequency is high, and the level of damage of the attacks are high. The risk of using centralized exchanges outweighs the risk of using Bitshares and trusting DPoS 1.0. DPoS 2.0 will be tested and audited, but DPoS 1.0 has never been successfully hacked.

Bitshares when it was first announced with through the same skepticism: https://bitcointalk.org/index.php?topic=279771.0
None of which played out.

https://raft.github.io/
http://martinfowler.com/articles/lmax.html