Abstract
In this note it is shown how a class of optimization problems with random terminal time, such as dynamic consumption/investment problems, can be transformed to equivalent infinite horizon optimization problems, even in the presence of boundary conditions representing bankruptcy and/or terminal bequest. In important special cases of interest, the transformation requires simply an upward revision of the discount rate by what is known as the hazard rate or the mortality rate. The result represents a significant generalization of the known results.
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Presman, E.L. (1997). Equivalence of Objective Functionals in Infinite Horizon and Random Horizon Problems. In: Optimal Consumption and Investment with Bankruptcy. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6257-3_10
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DOI: https://doi.org/10.1007/978-1-4615-6257-3_10
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