英文标题：
《The pricing of contingent claims and optimal positions in asymptotically
complete markets》
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作者：
Michail Anthropelos, Scott Robertson, Konstantinos Spiliopoulos
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最新提交年份：
2016
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英文摘要：
We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semi-martingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference price converges to a well defined limit, we prove that optimally taken positions become large in absolute value at a specific rate. We draw motivation from and make connections to Large Deviations theory, and in particular, the celebrated G\\\"{a}rtner-Ellis theorem. We analyze a series of well studied examples where this limiting behavior occurs, such as fixed markets with vanishing risk aversion, the basis risk model with high correlation, models of large markets with vanishing trading restrictions and the Black-Scholes-Merton model with either vanishing default probabilities or vanishing transaction costs. Lastly, we show that the large claim regime could naturally arise in partial equilibrium models.
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中文摘要：
我们研究了在不完全半鞅市场中，在套期保值误差和/或风险规避消失的情况下，未定权益的效用无差异价格和最优购买量。假设平均无差异价格收敛到一个定义明确的极限，我们证明了最优仓位在特定速率下绝对值变大。我们从大偏差理论中汲取动力并与之联系，尤其是，著名的G\\{a}埃利斯定理。我们分析了一系列研究充分的例子，其中出现了这种限制行为，例如风险厌恶消失的固定市尝高度相关的基本风险模型、交易限制消失的大型市场模型以及违约概率或交易成本消失的Black-Scholes-Merton模型。最后，我们证明了在部分均衡模型中，大索赔制度是自然产生的。
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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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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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