Faculty of Actuarial Science and Insurance Seminar with Francesco Menoncin

"Optimal consumption, portfolio, and health insurance in a dynamic framework"

Abstract:
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.

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