Minimizing the expected discounted time to ruin for a company managing N distinct funds with a “superclaims”process

Consider a company managing N distinct funds,each fund with its owm distinct initial reserve u i(i=1,2,... N) ,premium rates p i(i=1,2,...N) and distinct claims process X i(t).(i=1,2,...N) .An independent superclaims process corresponds that the company must honor,and choose to pay off via only one of the distinct uniquely until that fund is ruined,hence thesuperclaimswill be payed from another of the remaining funds(uniquely) until that fund is ruined,and so on.The company is  ruinedwhen its last remaining fund is ruined.In this paper we derive the optimal policy to minimize the expected discounted time until the company is ruined.