Three essays on risk and insurance
Previous writers have attempted to resolve the equity premium puzzle by employing a utility function that depends on current consumption minus (or relative to) past habit consumption. The first chapter points out that an individual's current utility may also depend upon how well off in the recent past he or she had expected to be today. Hence we add the concept "expectation formation" to the utility modification term in a model with a habit-formation utility function. We apply the model to equity premium puzzle and find that it is able to fit the data with a relatively low coefficient of relative risk aversion. Furthermore we fit the model to 40-year rolling samples and find that the estimated coefficient of risk aversion does not vary much as the sample changes. Hence we conclude that the model is able to resolve the equity premium puzzle. The second chapter presents a two-period model in which an individual can purchase insurance, save and borrow to protect herself against potential risk in the future. A model for insurance without the presence of capital market, and one for saving/borrowing without insurance are also discussed. We show that neither insurance nor precautionary saving/borrowing alone can generate a complete market analog, but both together can. We also show how optimal choices for insurance and saving/borrowing change when key factors in the environment change. The third chapter incorporates the ideas of habit formation and reference-dependent preference with a two-period model for insurance, saving and borrowing. I compare the results with the ones with a standard expected utility, and find that this model helps to explain all the phenomena of over-insured, under-saving and over-borrowing at the same time.