摘要翻译：
在L\'Evy过程驱动的市场中，我们重新讨论了Merton在状态依赖效用函数下的投资组合优化问题，推广了Karatzas等人的结果。Al.(1991)和Kunita(2003)。这个问题是用一个对偶变分问题来解决的，就像通常对非马尔可夫模型所做的那样。这里的一个主要特征是对偶问题的定义域具有一个显式的“参数化”，它建立在F\\Ollmer和Kramkov(1997)关于非负上鞅的乘法可选分解上。作为得到表示结果的一个关键步骤，我们证明了积分关于泊松随机测度的一个闭包性质，这是M\'Emin(1980)关于固定半鞅的积分的模拟性质的推广。对于一个过程$\zeta$和一个确定性函数$\vartheta$,我们显式地刻画了交易策略的可容许性，并证明了对偶解是一个风险中性的局部鞅，且对偶测度是有限原子数的原子，或对偶测度为$\delta S_{t}/S_{t^{-}}=\zeta_{t}\vartheta(\delta Z_{t}）.
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英文标题：
《State-dependent utility maximization in L\'evy markets》
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作者：
Jose E. Figueroa-Lopez and Jin Ma
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最新提交年份：
2009
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
  We revisit Merton's portfolio optimization problem under boun-ded state-dependent utility functions, in a market driven by a L\'evy process $Z$ extending results by Karatzas et. al. (1991) and Kunita (2003). The problem is solved using a dual variational problem as it is customarily done for non-Markovian models. One of the main features here is that the domain of the dual problem enjoys an explicit "parametrization", built on a multiplicative optional decomposition for nonnegative supermartingales due to F\"ollmer and Kramkov (1997). As a key step in obtaining the representation result we prove a closure property for integrals with respect to Poisson random measures, a result of interest on its own that extends the analog property for integrals with respect to a fixed semimartingale due to M\'emin (1980). In the case that (i) the L\'evy measure of $Z$ is atomic with a finite number of atoms or that (ii) $\Delta S_{t}/S_{t^{-}}=\zeta_{t} \vartheta(\Delta Z_{t})$ for a process $\zeta$ and a deterministic function $\vartheta$, we explicitly characterize the admissible trading strategies and show that the dual solution is a risk-neutral local martingale.
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PDF链接：
https://arxiv.org/pdf/0901.2070