论文标题
半明星的简化微积分：乘法补偿器和度量的变化
Simplified calculus for semimartingales: Multiplicative compensators and changes of measure
论文作者
论文摘要
该论文为复杂值的半明星提供了乘法补偿，并研究了其一些后果。结果表明，当这种补偿是有意义的时，在乘法补偿后，以独立增量为单独增量的任何复杂价值的半明星的随机指数变成了真实的群众。 Lévy-Khintchin公式的这种概括填补了文献中的现有空白。例如，它允许对符号随机指数的梅林转换的计算，而随机指数又在平均值 - 差异投资组合理论中具有实际应用。 Girsanov型基于多重补偿的半明星的结果简化了绝对连续度量变化的处理。例如，我们获得了在Lévy设置中流行的最小值度量的日志返回的特征函数。
The paper develops multiplicative compensation for complex-valued semimartingales and studies some of its consequences. It is shown that the stochastic exponential of any complex-valued semimartingale with independent increments becomes a true martingale after multiplicative compensation when such compensation is meaningful. This generalization of the Lévy--Khintchin formula fills an existing gap in the literature. It allows, for example, the computation of the Mellin transform of a signed stochastic exponential, which in turn has practical applications in mean--variance portfolio theory. Girsanov-type results based on multiplicatively compensated semimartingales simplify treatment of absolutely continuous measure changes. As an example, we obtain the characteristic function of log returns for a popular class of minimax measures in a Lévy setting.
