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You make some valid point but how can you self fund a case like this with high claims and not get lasered?
How did this turn out?
All the advice here seems correct but I would think that the most important factor would be to determine what is/has been driving the poor claims experience. With multiple years of 200% L/R's, it seems fairly likely that large claims, at least in part, are driving the experience. With multiple carriers declining to quote, large claims are very likely prevalent.
It would be very important to get your hands around the number and nature of the large claimants. That is what I would do and that would determine the right course of action, not only at the current renewal but over the next year or two.
My advice would be to partner with someone who has access to self-funded markets (a TPA or large group specialist) and go from there. While the group isn't all that big at 80 EEs, self funding should be an option now, or in the future. You may be able to find an appropriate self-funded option with separate Spec levels for the large claimant(s). Then again, you may not.
The key is that even if the high fully insured renewal may very well be the best (or only) recommendation, at some point the large claims will resolve in full or in part, and you will have a reasonably manageable group health risk. I would not wait until that time to start to manage the health risk of the group. At that point, anyone who can get a quote can do as good a job as the incumbent broker.