A Bound on the Probability of Ruin in Merton’s Model


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We consider a modified Merton’s model of optimal consumption that allows for the utility of continuous and terminal consumption. An explicit solution of the Hamilton-Jacoby-Bellman equation is found. An upper bound is constructed on the probability of an event involving either investor ruin or negative consumption.

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V. Morozov

Faculty of Computational Mathematics and Cybernetics, Moscow State University

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Email: vmorosov@mail.ru
俄罗斯联邦, Moscow

V. Babin

Faculty of Computational Mathematics and Cybernetics, Moscow State University

Email: vmorosov@mail.ru
俄罗斯联邦, Moscow

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