Optimal Consumption-Insurance problems - A study of savings protections – University of Copenhagen

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Optimal Consumption-Insurance problems - A study of savings protections

Specialeforsvar ved Anders Druedahl

Titel:  Optimal Consumption-Insurance problems - A study of savings protections 

Abstract: Utility optimization of households deciding upon consumption and life insurance are studied. In particular, optimality of the life insurance product savings protection is investigated. Distinguishing between private wealth and institutional wealth, partial equili-brium optimal controls are specified on closed form in continuous-time. This is done firstly in the survival model and then generalized into a multi-state Markov chain. Analytical characterizations of agents who prefer savings protection are found to be unattainable for sophisticated agents with labour income. For various naive agents (and sophisticated agents without labour income), the recurring characteristic for agents demanding savings protection is disclosed to be equal appreciation of consumption regardless of the size of the household. Budget constraints are inferred in a discrete-time Markov model and optimal controls are estimated for two identical agents using numerical dynamic program-ming. It appears that prohibiting negative institutional wealth has a dampening effect on the demand for life insurance. As a consequence, the marginal utility loss from constraints is so extensive that it overshadows the marginal utility loss of savings protection. However, the utility loss arising from savings protection is still considerable


Vejleder:  Mogens Steffensen
Censor:    Kenneth Bruhn, PenSam