I don't think that the exposure is specifically to litigation, though that would be one way of incurring cost, or to risk, as the risk is what was insured and has, presumably, already been incurred by the insured party.

By "resolving claims in a timely manner", exposure to administrative and legal costs would be reduced and so would the amount paid out in settling claims, as customers would sometimes settle for a lesser amount in order to receive it promptly and without hassle.