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A life insurance model with asymmetric time preferences

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We build a life insurance model in the tradition of Richard (1975) and Pliska and Ye (2007). Two agents purchase
life insurance by continuously paying two premiums. At the random time of death of an agent, the life insurance
payment is added to the household wealth to be used by the other agent. We allow for the agents to discount
future utilities at different rates, which implies that the household has inconsistent time preferences. To solve the
model, we employ the equilibrium of Ekeland and Lazrak (2010), and we derive a new dynamic programming
equation which is designed to find this equilibrium for our model. The most important contribution of the paper
is to combine the issue of inconsistent time preferences with the presence of several agents. We also investigate
the sensitivity of the behaviors of the agents to the parameters of the model by using numeric analysis. We find,
among other things, that while the purchase of life insurance of one agent increases in her own discount rate, it
decreases in the discount rate of the other agent.

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Insurance Mathematics and Economics, 2024, vol. 119, p. 17-31

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Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial)

# metadata.dc.title[].value
A life insurance model with asymmetric time preferences