The pricing of contingent claims and optimal positions in asymptotically complete markets
The pricing of contingent claims and optimal positions in asymptotically complete markets
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渐进完全市场中或有债权的定价和最优头寸
DOI：
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发表时间：
2015
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通讯作者：
K. Spiliopoulos
中科院分区：
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作者：
Michail Anthropelos;Scott Robertson;K. Spiliopoulos
研究了不完全半鞅市场中套期保值误差和风险厌恶为零时未定权益的效用无差别价格和最优购买量。假设平均无差别价格收敛到一个明确定义的限制，我们证明了最佳采取的立场成为大的绝对值在一个特定的速度。我们从大偏差理论，特别是著名的G”{a}rtner-Ellis定理中汲取动力并建立联系。我们分析了一系列研究的例子，这种限制行为的发生，如固定市场与消失的风险厌恶，高相关性的基础风险模型，模型的大型市场与消失的交易限制和Black-Scholes-Merton模型，无论是消失的违约概率或消失的交易成本。最后，我们表明，大索赔制度可以自然地出现在部分均衡模型。
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.