英文标题：
《Optimal investment and consumption with downside risk constraint in
jump-diffusion models》
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作者：
Thai Nguyen
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最新提交年份：
2016
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英文摘要：
This paper extends the results of the article [C. Kl\\\"{u}ppelberg and S. M. Pergamenchtchikov. Optimal consumption and investment with bounded downside risk for power utility functions. In Optimality and Risk: {\\it Modern Trends in Mathematical Finance. The Kabanov Festschrift}, pages 133-169, 2009] to a jump-diffusion setting. We show that under the assumption that only positive jumps in the asset prices are allowed, the explicit optimal strategy can be found in the subset of admissible strategies satisfying the same risk constraint as in the pure diffusion setting. When negative jumps probably happen, the regulator should be more conservative. In that case, we suggest to impose on the investor\'s portfolio a stricter constraint which depends on the probability of having negative jumps in the assets during the whole considered horizon.
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中文摘要：
本文推广了[C.Kl \\“{u}ppelberg和S.M.Pergamenchchikov.电力效用函数具有有限下行风险的最优消费和投资.最优性和风险：{it现代数学金融趋势.Kabanov Festschrift}，第133-169页，2009]跳转扩散设置。我们证明了在只允许资产价格正跳的假设下，在满足与纯扩散环境相同的风险约束的可容许策略子集中可以找到显式最优策略。当可能出现负增长时，监管机构应该更加保守。在这种情况下，我们建议对投资者的投资组合施加更严格的约束，这取决于在整个考虑期内资产出现负跳的概率。
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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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