Market insurance and endogenous saving with multiple loss states

•When an individual has no access to a capital market, the individual can purchase partial or no insurance given actuarially fair premium, and full or over-insurance given unfavorable premium.•Insurance is neither an inferior good nor a Giffen good without considering capital market. An increase in concavity of the utility function does not always increase insurance demand.•Only if the individual has access to a capital market does an actuarially fair premium lead to full insurance.•Insurance can be a Giffen good under decreasing absolute risk aversion (DARA) when a savings opportunity exists. An increase in concavity of the utility function leads to an increase in insurance demand and a decrease in saving. The standard one-period model for insurance demand does not consider the interaction between the present and the future. Reflecting this observation, we analyze intertemporal insurance demand and saving in a two-period model with multiple loss states. When an individual has no access to a capital market, we first find that an actuarially fair premium does not guarantee full insurance in general, unlike in the standard approach. Income stream and discount factors are also important in determining insurance demand. Second, insurance is neither an inferior good nor a Giffen good. Third, an increase in concavity of the utility function does not always lead to an increase in insurance demand. The current income level and changes in downside risk aversion affect insurance demand. When the individual has access to a capital market, we further have the following observations. Fourth, an actuarially fair premium leads to full insurance. Fifth, insurance is an inferior good and can be a Giffen good under decreasing absolute risk aversion (DARA). An increase in the interest rate leads to a lower insurance demand and a higher saving when the relative risk aversion is less than unity. Lastly, an increase in concavity of the utility function leads to an increase in insurance demand and a decrease in saving. In conjunction, our findings point to the fact that the standard results are not obtainable if insurance demand is considered in isolation from the capital market.