“…Pioneered by Arrow [1,2,3], many articles on optimal insurance problem under various constraints, with consideration of application in personal lines or commercial lines, have been contributed to the literature in this field. Typical papers include but are not limited to Smith [31], Mossin [25], Spence and Zeckhauser [32], Raviv [30], Doherty and Schlesinger [8], Gollier and Schlesinger [16], Young [37], Moore and Young [24], Lee [19], Zhou and Wu [42], Zhou et al [43], Bernard et al [4], Promislow and Young [28], Lu et al [22], Xu et al [35], Ho et al [18], Fan [11] and Zhang and Wu [40]. Most of the aforementioned papers assume that the individual would suffer a random loss and pay premium to the insurer for indemnity in case that the loss occurs.…”