Maximizing the Expected Time to Ruin for a Company Operating N Distinct Funds with a "Superclaims" Process

Consider a company operating N distinct funds, each fund with its own distinct initial reserve, premium rates and distinct claims process. Superimposed upon these is an independent "superclaims" process which the company must honor, and chooses to pay off via only one of the distinct funds uniquely until that fund is ruined, whereupon the "superclaims" will be honored 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 maximize the expected time until the company is ruined. The policy is of index form.