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We solve the problem of an agent who maximizes the expected discounted
(HARA) utility of his inter-temporal consumption over a stochastic life time horizon (mortality risk). The agent can invest on a complete and arbitrage free financial market, and faces a health risk which takes the form of a jump Poisson process. In case of illness, some wealth is lost. The agent may hedge against this risk by subscribing an insurance contract, on which we assume there exists a mark-up. We find a closed form solution for the optimal consumption, the optimal portfolio, and the optimal insurance hedge. Finally, some numerical simulations show the behavior of the optimal solutions over time.
Cass Business School, 106 Bunhill Row
106 Bunhill Row, London EC1Y 8TZ, UK
University of Brescia, Department of Economics and Management
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