Non Quadratic Local Risk-Minimization for Hedging Contingent Claims in Incomplete Markets
Non Quadratic Local Risk-Minimization for Hedging Contingent Claims in Incomplete Markets
复制标题
不完全市场中对冲或有债权的非二次局部风险最小化
DOI：
10.2139/ssrn.1647626
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Nicolas Millot
中科院分区：
文献类型：
--
作者：
F. Abergel;Nicolas Millot
在不完全市场中，我们引入了一个新的标准来进行未定权益套期保值。我们的方法接近Schweizer [Stochastic Process.应用程序、37（1991），pp. 339-363]，因为它使用局部风险最小化策略的概念。但我们的目标是更一般的定义为一个一般的，不一定二次，局部成本过程的凸函数的局部风险。在离散时间和连续时间两种情况下，我们分别推导出了相应的最优策略和价值函数.最后，我们给出了应用我们的套期保值方法在随机波动率的情况下，以及在跳跃扩散的情况下。我们处理的是单一的交易资产，但我们的方法可以推广到处理依赖于多个资产的索赔。
We introduce a new criterion to perform hedging of contingent claims in incomplete markets. Our approach is close to the one proposed by Schweizer [Stochastic Process. Appl., 37 (1991), pp. 339-363] in that it uses the concept of locally risk-minimizing strategies. But we aim at being more general by defining the local risk as a general, nonnecessarily quadratic, convex function of the local cost process. We derive the corresponding optimal strategies and value function in both discrete and continuous time settings. Finally we give an application of our hedging method in the stochastic volatility case as well as in the jump diffusion case. We work with a single traded asset, but our approach may be generalized to deal with claims depending on multiple assets.