英文标题：
《Multi-asset consumption-investment problems with infinite transaction
costs》
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作者：
David Hobson and Yeqi Zhu
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最新提交年份：
2014
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英文摘要：
The subject of this paper is an optimal consumption/optimal portfolio problem with transaction costs and with multiple risky assets. In our model the transaction costs take a special form in that transaction costs on purchases of one of the risky assets (the endowed asset) are infinite, and transaction costs involving the other risky assets are zero. Effectively, the endowed asset can only be sold. In general, multi-asset optional consumption/optimal portfolio problems are very challenging, but the extra structure we introduce allows us to make significant progress towards an analytical solution. For an agent with CRRA utility we completely characterise the different types of optimal behaviours. These include always selling the entire holdings of the endowed asset immediately, selling the endowed asset whenever the ratio of the value of the holdings of the endowed asset to other wealth gets above a critical ratio, and selling the endowed asset only when other wealth is zero. This characterisation is in terms of solutions of a boundary crossing problem for a first order ODE. The technical contribution is to show that the problem of solving the HJB equation, which is a second order, non-linear PDE subject to smooth fit at an unknown free boundary, can be reduced to this much simpler problem involving an explicit first order ODE. This technical contribution is at the heart of our analytical and numerical results, and allows us to prove monotonicity of the critical exercise threshold and the certainty equivalent value in the model parameters.
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中文摘要：
本文的主题是一个具有交易成本和多风险资产的最优消费/最优投资组合问题。在我们的模型中，交易成本有一种特殊形式，即购买其中一种风险资产（被赋予的资产）的交易成本是无限的，而涉及其他风险资产的交易成本为零。实际上，捐赠资产只能出售。一般来说，多资产可选消费/最优投资组合问题非常具有挑战性，但我们引入的额外结构允许我们在分析解决方案方面取得重大进展。对于具有CRRA效用的代理，我们完全描述了不同类型的最佳行为。这些措施包括始终立即出售全部捐赠资产，在捐赠资产与其他财富的价值之比超过临界比率时出售捐赠资产，以及仅在其他财富为零时出售捐赠资产。这种特征是一阶常微分方程边界交叉问题的解。技术贡献在于表明，求解HJB方程的问题可以简化为一个简单得多的问题，该方程是一个二阶非线性偏微分方程，在未知自由边界处进行平滑拟合。这项技术贡献是我们分析和数值结果的核心，它使我们能够证明临界运动阈值和模型参数中确定性等效值的单调性。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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