论文标题
经典金融模型中风险的量化
Quantification of Risk in Classical Models of Finance
论文作者
论文摘要
本文提高了衍生品的定价以及包括风险的水平的最佳控制问题。我们采用嵌套的风险措施来量化风险，研究经典模型中嵌套风险度量的限制行为，并表征了规避风险限制的存在。结果，我们证明嵌套极限是独特的，无论最初选择的风险度量如何。在经典模型中，风险规避会导致风险溢价流，可与股息支付相当。在这种情况下，我们将连贯的风险度量与现代投资组合理论的夏普比率联系起来，并提取Z-Spread（一种经济学中广泛接受的数量，以对冲风险。然后，将欧洲期权定价的结果扩展到规避风险的美国选择，我们研究风险对价格的影响以及行使期权的最佳时间。我们还将默顿的最佳消费问题扩展到规避风险的环境。
This paper enhances the pricing of derivatives as well as optimal control problems to a level comprising risk. We employ nested risk measures to quantify risk, investigate the limiting behavior of nested risk measures within the classical models in finance and characterize existence of the risk-averse limit. As a result we demonstrate that the nested limit is unique, irrespective of the initially chosen risk measure. Within the classical models risk aversion gives rise to a stream of risk premiums, comparable to dividend payments. In this context we connect coherent risk measures with the Sharpe ratio from modern portfolio theory and extract the Z-spread -- a widely accepted quantity in economics to hedge risk. The results for European option pricing are then extended to risk-averse American options, where we study the impact of risk on the price as well as the optimal time to exercise the option. We also extend Merton's optimal consumption problem to the risk-averse setting.
