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Bubbles in assets with finite life
Mathematics and Financial Economics ( IF 1.6 ) Pub Date : 2019-01-01 , DOI: 10.1007/s11579-018-0233-4
Henri Berestycki , Cameron Bruggeman , Regis Monneau , José A. Scheinkman

We study the speculative value of a finitely lived asset when investors disagree and short sales are limited. In this case, investors are willing to pay a speculative value for the resale option they obtain when they acquire the asset. Using martingale arguments, we characterize the equilibrium speculative value as a solution to a fixed point problem for a monotone operator \(\mathbb F\). A Dynamic Programming Principle applies and is used to show that the minimal solution to the fixed-point problem is a viscosity solution of a naturally associated (non-local) obstacle problem. Combining the monotonicity of the operator \({\mathbb {F}}\) and a comparison principle for viscosity solutions to the obstacle problem we obtain several comparison of solution results. We also use a characterization of the exercise boundary of the obstacle problem to study the effect of an increase in the costs of transactions on the value of the bubble and on the volume of trade, and in particular to quantify the effect of a small transaction (Tobin) tax.

中文翻译:

有限寿命的资产泡沫

当投资者不同意并且卖空受到限制时,我们研究有限寿资产的投机价值。在这种情况下,投资者愿意为购买资产时获得的转售权支付投机价值。通过使用ting论点,我们将均衡投机值表征为单调算子\(\ mathbb F \)的不动点问题的解决方案。应用了动态规划原理,该原理用于显示定点问题的最小解决方案是自然关联的(非局部)障碍问题的粘性解决方案。结合运算符\({\ mathbb {F}} \)的单调性并通过对障碍问题的粘性解的比较原理,我们得到了几种解结果的比较。我们还使用障碍问题的执行边界的特征来研究交易成本增加对泡沫价值和交易量的影响,尤其是量化小额交易的影响(托宾)税。
更新日期:2019-01-01
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