HEDGING UNDER ARBITRAGE
论文证明在连续时间马尔可夫市场模型中，即使不存在等价局部鞅测度，delta对冲仍能以最小初始资本复制给定终期收益，并构造了替代概率测度。
It is shown that delta hedging provides the optimal trading strategy in terms of minimal required initial capital to replicate a given terminal payoff in a continuous‐time Markovian context. This holds true in market models in which no equivalent local martingale measure exists but only a square‐integrable market price of risk. A new probability measure is constructed, which takes the place of an equivalent local martingale measure. To ensure the existence of the delta hedge, sufficient conditions are derived for the necessary differentiability of expectations indexed over the initial market configuration. The phenomenon of “bubbles,” which has recently been frequently discussed in the academic literature, is a special case of the setting in this paper. Several examples at the end illustrate the techniques described in this work.