Local risk-minimization for multidimensional assets and payment streams
Local risk-minimization for multidimensional assets and payment streams
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DOI：
10.4064/bc83-0-13
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发表时间：
2008
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影响因子：
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通讯作者：
M. Schweizer
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文献类型：
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作者：
M. Schweizer
在不完全金融市场中，最早的套期保值和定价概念之一是局部风险最小化的二次准则。然而，迄今为止，定义和理论仅针对单一（一维）风险资产的情况建立。我们将这种方法推广到一般的多维情形，并证明了局部风险最小化策略的基本鞅刻画结果仍然成立。与现有的文献相比，自包含的介绍更加精简，并且不再需要一些早先强加的技术条件。作为一个小的扩展，我们展示了如何支付流（而不是最终支付），以及可以处理。
One of the earliest concepts for hedging and pricing in incomplete flnancial markets has been the quadratic criterion of local risk-minimization. However, deflnitions and theory have so far been established only for the case of a single (one-dimensional) risky asset. We extend the approach to a general multidi- mensional setting and prove that the basic martingale characterization result for locally risk-minimizing strategies still holds true. In comparison with exist- ing literature, the self-contained presentation is more streamlined, and a number of earlier imposed technical conditions are no longer needed. As a minor ex- tension, we show how payment streams (instead of flnal payofis only) can be handled as well.