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Optimal Consumption and Investment with Bankruptcy
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The problem of optimal consumption and investment is concerned with the decisions of a single agent endowed with some initial wealth who seeks to maximize total expected discounted utility of consumption. The decisions are the rate of consumption and the allocation of their wealth directed to risky and risk-free investments over time. The problem was first studied by Paul Samuelson and Robert Merton in 1969; however none of their formulations took into account the possibility that an agent might go bankrupt in the process. In a set of articles published in 1979 and 1983, Suresh Sethi and various co-authors explicitly introduced a bankruptcy value/penalty in the consumption/investment model. In addition, they also introduced a nonzero subsistence consumption level, which makes the consideration of bankruptcy even more important. This provided the ability to deal mathematically with the problems of bankruptcy in the study of consumption and investment. Optimal Consumption and Investment with Bankruptcy provides a useful frame for deepening our understanding of the consumption and portfolio selection behavior of individuals and households.
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