Analysis of Collateralized Debt Obligation Scheme Applied to Newsboy Problem

Abstract

As a sequel to the original paper by the same authors, Isogai, Ohashi, and Sumita [5], this paper examines the effect of the collateralized debt obligation (CDO) scheme applied to the classical newsboy problem (NBP). The distribution function of the profit with CDO is derived explicitly as a function of the orderquantityQ. Sufficient conditions are established under which the optimal solution for the value at risk (VaR) problem with CDO is superior or inferior to that without CDO. Furthermore, the VaR problem of NBP without CDO is analyzed in detail for the case of the exponentially distributed demand, deriving the optimal solution **NBP Q and ** NBP explicitly. Assuming that the stochastic demand D is exponentially distributed, extensive numerical experiments reveal that the overall effect of CDO is present when the underlying risk for the opportunity loss is rather large