An Optimal Investment/Consumption Model with Borrowing
An Optimal Investment/Consumption Model with Borrowing
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DOI：
10.1287/moor.16.4.802
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发表时间：
1991-10
期刊：
影响因子：
--
通讯作者：
W. Fleming;T. Zariphopoulou
中科院分区：
文献类型：
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作者：
W. Fleming;T. Zariphopoulou
本文考虑单个智能体的消费和投资决策问题。财富分为无风险资产和具有对数布朗运动价格波动的风险资产。不允许卖空，但允许以高于无风险资产收益率的利率借款。最大总贴现预期效用函数 U 的动态规划微分方程的显式解仅在 HARA 情况下可用。然而，使用粘性求解方法，可以发现对于小财富 x 和大财富 x 的价值函数 v ( x ) 的渐近行为。
This paper considers a consumption and investment decision problem for a single agent. Wealth is divided between a riskless asset and a risky asset with logarithmic Brownian motion price fluctuations. Short-selling is not allowed, but borrowing is allowed at rate exceeding the rate of return on the riskless asset. An explicit solution of the dynamic programming differential equation for the maximum total discounted expected utility function U is available only in the HARA case. However, using viscosity solution methods the asymptotic behavior of the value function v ( x ) is found for small wealth x and for large wealth x .