Earlier studies in insurance demand (e.g., Arrow, 1963; Harris and Raviv, 1978; Holmström, 1979) mostly focus on single (pure) risk and using insurance as the only tool of risk reduction. Later studies (e.g., Gould, 1969; Mayers and Smith, 1983; Briys, 1986, 1988, Gollier, 1994 etc.) then view pure risk as one of the risks in many market risks; thereby, it is nature to derive the insurance decision which is not independent of other financial decisions. Dionne and Doherty (2000) considered several risks, including pure risk, investment risk, background risk and the risk from information asymmetry simultaneously, and pointed out that only insurance policy is not sufficient to manage risks efficiently. Other financial instruments should be jointly used with insurance.
To date, many researchers have devoted to the study regarding the integrated decision-making of insurance and portfolio choice. For example, Mayers and Smith (1983) is one of the earliest papers to solve the optimal insurance demand for an agent who also invests his wealth in financial stock and bond in which insurance risk and financial assets are assumed to be correlated. Bryis (1986) later analyzed insurance demand along with investment and consumption decisions in the context of Merton’s (1969) portfolio choice problem. Gollier (1994) investigated the strategy of bearing insurable risk and showed how precautionary saving can dominate insurance under certain conditions. Meyer and Ormiston (1995) derived the optimal insurance in an aggregate financial portfolio framework. In their study, insurance quantity decision is considered as one of portfolio selection decisions which is used to reduce the quantity of risky asset.
Typically, risk can be classified into two types, i.e., the financial risk mostly caused by the uncertainty of securities return, and the non-financial insurable “background risk”, including pure loss, inflation, labor income risk, political turmoil and natural disasters etc. (see also Doherty and Schlesinger, 1983; Heaton and Lucas, 1997; 2000). Several recent studies (Heaton, Lucas, 1997; 2000; Viceira, 2001) have derived the optimal asset allocation and consumption rate for a representative agent by taking into account the effect of background risk. Many empirical evidences (e.g., Campbell et al., 1999; Campbell and Viceira, 2002; Jagannathan et al., 1998) found that background risk may be positively correlated with the securities investment risks. Under this assumption, Viceira (2001) showed that the increase of labor income risk may turn to reduce investor’s consumption and the holding of risky asset.
However, not all background risk is uninsurable. A few types of background risk can be transferred through insurance policies in which insurance company can further pool the risk by writing a large numbers of policies and/or simply reduce the risk by reinsurance. For example, an agent can purchase unemployment insurance policy to reduce part of labor income risk. On the other hand, there are many other types of background risk which can be transferred neither by insurance nor by financial instruments, such as domestic political turmoil.
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Asset Allocation and Consumption Rule in the Presence of Background Risk and Insurance Market
