英文标题：
《A BSDE arising in an exponential utility maximization problem in a pure
jump market model》
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作者：
Carla Mereu and Robert Stelzer
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最新提交年份：
2016
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英文摘要：
We consider the problem of utility maximization with exponential preferences in a market where the traded stock/risky asset price is modelled as a L\\\'evy-driven pure jump process (i.e. the driving L\\\'evy process has no Brownian component). In this setting, we study the terminal utility optimization problem in the presence of a European contingent claim. We consider in detail the BSDE (backward stochastic differential equation) characterising the value function when using an exponential utility function. First we analyse the well-definedness of the generator. This leads to some conditions on the market model related to conditions for the market to admit no free lunches. Then we give bounds on the candidate optimal strategy. Thereafter, we discuss the example of a cross-hedging problem and, under severe assumptions on the structure of the claim, we give explicit solutions. Finally, we establish an explicit solution for a related BSDE with a suitable terminal condition but a simpler generator.
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中文摘要：
我们考虑在一个交易股票/风险资产价格被建模为勒夫驱动的纯跳跃过程（即，驱动的勒夫过程没有布朗成分）的市场中，具有指数偏好的效用最大化问题。在此背景下，我们研究了欧式未定权益下的终端效用优化问题。我们详细考虑了BSDE（倒向随机微分方程）在使用指数效用函数时表征值函数的特性。首先，我们分析了生成器的良定性。这导致了市场模型中的一些条件，即市场不允许免费午餐的条件。然后给出候选最优策略的界。然后，我们讨论了交叉套期保值问题的例子，并在对索赔结构的严格假设下，给出了明确的解决方案。最后，我们建立了一个相关BSDE的显式解，该解具有合适的终端条件，但生成器更简单。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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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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