A model-free approach to continuous-time finance
A model-free approach to continuous-time finance
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连续时间金融的无模型方法
DOI：
10.1111/mafi.12370
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发表时间：
2023
影响因子：
1.6
通讯作者：
Chiu H
中科院分区：
文献类型：
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作者：
Chiu H
我们提出了一种基于因果函数演算的连续时间金融的路径方法。我们的框架不依赖于任何概率概念。我们引入了连续时间自融资投资组合的定义，该定义不依赖于任何积分概念，并表明自融资投资组合的价值属于一类非预期泛函，它们是鞅的路径类似物。我们表明，如果市场情景集在某些操作下保持稳定的意义上是通用的，那么这种自融资策略就不会产生套利。然后，我们考虑在一组通用场景中对冲路径依赖收益的问题。将Rufus Isaacs的转移原理应用到微分博弈中，我们得到了超级对冲成本的路径动态规划原理。我们证明超级对冲成本的特征是路径依赖方程的解。对于亚洲选项，我们获得了一个明确的解决方案。
We present a pathwise approach to continuous‐time finance based on causal functional calculus. Our framework does not rely on any probabilistic concept. We introduce a definition of continuous‐time self‐financing portfolios, which does not rely on any integration concept and show that the value of a self‐financing portfolio belongs to a class of nonanticipative functionals, which are pathwise analogs of martingales. We show that if the set of market scenarios isgenericin the sense of being stable under certain operations, such self‐financing strategies do not give rise to arbitrage. We then consider the problem of hedging a path‐dependent payoff across a generic set of scenarios. Applying the transition principle of Rufus Isaacs in differential games, we obtain a pathwise dynamic programming principle for the superhedging cost. We show that the superhedging cost is characterized as the solution of a path‐dependent equation. For the Asian option, we obtain an explicit solution.