Continuous implies there is no discrete distinction between members, contiguous impies that the various members of the set are next to each other.
As an example, the visible spectrum of light is a continuous set, but when most people draw a rainbow, they put several colors right next to each other in a contiguous set.
Files are stored as discrete blocks on a drive, with the physical sectors lying one up against the other, but with discrete boundaries between each packet. Since each packet has a header, there is a discrete boundary, and as such, the correct word is contiguous.
A regular Google search gives about 350,000 hits for ‘indifferent between’, while a Google books search gives about 120,000 hits.
I cannot find any dictionary entries that include examples or citations with this usage, but it does appear to be in actual use, if not all that common.
As such, I wouldn’t classify it as ‘truly ungrammatical’, but rather perhaps as ‘best avoided in contexts where you wish to steer clear of potentially controversial grammar’.
In your particular phrase, I would suggest:
X is indifferent to whether (we do/he does/etc.) Y or Z
Or, even more plainly spoken:
X does not care whether (we do/he does/etc.) Y or Z
Edit to reflect edited question:
With the context now known, I would suggest recasting the sentence as follows (vel sim):
The risk adjustment should reflect the compensation that an insurer requires for bearing this uncertainty and reflects the point at which the insurance company considers fulfilling an insurance contract with a range of possible outcomes and fulfilling a liability with fixed cash flows (to be) equal options.
Best Answer
I think employment with is more idiomatic and is backed up by a google Ngram search.