Discrete-time hedging produces a residual P&L, namely the tracking error. The major problem is to get valuation/hedging policies minimising this error. We evaluate the risk between trading dates through a function penalising profits and losses asymmetrically. After deriving the asymptotics from a discrete-time risk measurement for a large number of trading dates, we derive the optimal strategies minimising the asymptotic risk in a continuous-time setting. We characterise optimality through a class of fully nonlinear partial differential equations (PDEs). Numerical experiments show that the optimal strategies associated with the discrete and the asymptotic approaches coincide asymptotically.

中文翻译：

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使用非对称风险函数的期权估值和对冲：通过完全非线性偏微分方程的渐近最优性

离散时间套期保值会产生残余盈亏，即跟踪误差。主要的问题是获得使该错误最小化的评估/对冲政策。我们通过不对称惩罚损益的函数来评估交易日之间的风险。从大量交易日期的离散时间风险度量中得出渐近性之后，我们得出了在连续时间设置中最小化渐近风险的最优策略。我们通过一类完全非线性的偏微分方程（PDE）表征最优性。数值实验表明，与离散和渐近方法相关的最优策略是渐近一致的。