英文标题：
《Indifference pricing for Contingent Claims: Large Deviations Effects》
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作者：
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 non-traded contingent claim in an incomplete semi-martingale market with vanishing hedging errors. We make connections with the theory of large deviations. We concentrate on sequences of semi-complete markets where in the $n^{th}$ market, the claim $B_n$ admits the decomposition $B_n = D_n+Y_n$. Here, $D_n$ is replicable by trading in the underlying assets $S_n$, but $Y_n$ is independent of $S_n$. Under broad conditions, we may assume that $Y_n$ vanishes in accordance with a large deviations principle as $n$ grows. In this setting, for an exponential investor, we identify the limit of the average indifference price $p_n(q_n)$, for $q_n$ units of $B_n$, as $n\\rightarrow \\infty$. We show that if $|q_n|\\rightarrow\\infty$, the limiting price typically differs from the price obtained by assuming bounded positions $\\sup_n|q_n|<\\infty$, and the difference is explicitly identifiable using large deviations theory. Furthermore, we show that optimal purchase quantities occur at the large deviations scaling, and hence large positions arise endogenously in this setting.
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中文摘要：
研究了套期保值误差为零的不完全半鞅市场中非交易或有权益的效用无差异价格和最优购买量。我们与大偏差理论联系在一起。我们专注于半完全市场序列，其中在$n^{th}$市场中，索赔$B_n$允许分解$B_n=D_n+Y_n$。在这里，$D_n$可以通过交易标的资产$S_n$来复制，但$Y_n$独立于$S_n$。在广泛的条件下，我们可以假设$Y_n$随着$n$的增长而根据大偏差原则消失。在这种情况下，对于指数型投资者，我们将平均无差异价格$p_n（q_n）$的限制确定为$n\\rightarrow\\infty$。我们证明，如果$|q|n | \\rightarrow\\infty$，极限价格通常不同于通过假设有界位置$\\sup|n | q|n<\\infty$获得的价格，并且使用大偏差理论可以明确地识别这种差异。此外，我们还表明，最优采购量出现在大偏差缩放时，因此在这种情况下，大仓位是内生的。
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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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