Hidden regular variation for point processes and the single/multiple large point heuristic

We consider regular variation for marked point processes with independent heavy-tailed marks and prove a single large heuristic: the limit measure is concentrated on cone of measures one point. then investigate successive hidden removing at most k points, k≥1, multiple phenomenon: k+1 points. show how these results imply in Skorokhod space associated risk process, connection single/multiple heuristic from (Ann. Probab. 47 (2019) 3551–3605). Finally, we provide an application to theory reinsurance model where largest claims are covered study asymptotic behavior residual risk.