Do LLCs each have new/separate insurance history/records?

[Payman A.]

Hi all,

Looking at another possible claim at one of the rental SFRs and though it is basically a continuation of the previous issue, it would be the 2nd claim in about 7-8 months.  Needless to say, I'm concerned about premiums on not just this policy but other properties as they are all under my name.  Would transferring existing properties to new LLCs give each a fresh insurance history and keep them separate from other policies in case of future claims as well?  

I'd appreciate your thoughts/suggestions.