具有工业投资机会和非线性收益的离散时间金融模型中的最优消费
Optimal consumption in discrete-time financial models with industrial investment opportunities and nonlinear returns
摘要：
我们考虑一个一般的离散时间金融市场，交易成本成比例，如[Kabanov，Stricker和Rásonyi金融和随机7（2003）403- 411]和[Schachermayer Math. Finance 14（2004）19- 48]。除了通常的金融资产投资外，我们假设代理人可以将其部分财富投资于产生非线性随机回报的工业项目。研究有限时间内消费效用最大化问题。非金融资产收益率的非线性是其主要困难所在。我们的主要结果是表明，存在的效用最大化问题。作为一个中间步骤，我们证明了一个强大的无套利性质下的可达到索赔的集合$A_T$的封闭性类似于在[Schachermayer Math. Finance 14（2004）19- 48]中介绍的，并在[Kabanov，Stricker and Rásonyi Finance and Stochastics 7（2003）403- 411]中进一步讨论。这使我们能够为$A_T$提供一个双重公式。
英文摘要：
We consider a general discrete-time financial market with proportional transaction costs as in [Kabanov, Stricker and Rásonyi Finance and Stochastics 7 (2003) 403--411] and [Schachermayer Math. Finance 14 (2004) 19--48]. In addition to the usual investment in financial assets, we assume that the agents can invest part of their wealth in industrial projects that yield a nonlinear random return. We study the problem of maximizing the utility of consumption on a finite time period. The main difficulty comes from the nonlinearity of the nonfinancial assets' return. Our main result is to show that existence holds in the utility maximization problem. As an intermediary step, we prove the closedness of the set $A_T$ of attainable claims under a robust no-arbitrage property similar to the one introduced in [Schachermayer Math. Finance 14 (2004) 19--48] and further discussed in [Kabanov, Stricker and Rásonyi Finance and Stochastics 7 (2003) 403--411]. This allows us to provide a dual formulation for $A_T$.
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