The problem of optimal insurance with background risk was first studied by Mayers and Smith (1983), who investigated the optimal proportion rate of quota-share insurance together with the demand of financial assets. In the past thirty years, this problem has been widely studied and has attracted great attentions from the academics. In this talk, we give an overview of key contributions to this topic. In particular, we discuss the main challenges and recent developments of deriving optimal insurance solutions satisfying the principle of indemnity and incentive compatibility.
