Abstract
An agent can distribute his wealth between two investments, one with a fixed rate of return r and the other with a random rate of return with mean r. The risk inherent in the second investment is modeled as a martingale. The agent seeks to maximize total discounted utility from consumption over an infinite horizon. It is shown that previously obtained results in which risk was modeled as a Wiener process provide bounds on the value function in the present context. Conditions are given under which these bounds are attained, and examples are provided.
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Lehoczky, J.P., Shreve, S.E. (1997). A Martingale Formulation for Optimal Consumption/Investment Decision Making. In: Optimal Consumption and Investment with Bankruptcy. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6257-3_15
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DOI: https://doi.org/10.1007/978-1-4615-6257-3_15
Publisher Name: Springer, Boston, MA
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