A model-free approach to continuous-time finance

IF 1.6 3区 经济学 Q3 BUSINESS, FINANCE
Henry Chiu, Rama Cont
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引用次数: 2

Abstract

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 is generic in 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.

连续时间金融的无模型方法
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组合的定义,该定义不依赖于任何积分概念,并证明了自融资组合的价值属于一类非预期泛函,这类泛函是鞅的路径类比。我们证明,如果市场情景集在某些操作下是稳定的,那么这种自融资策略不会产生套利。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。应用鲁弗斯·艾萨克在微分对策中的转移原理,得到了超套期保值代价的路径动态规划原理。我们证明了超套期保值成本的特征是一个路径相关方程的解。对于亚洲期权,我们得到了一个显式解。
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来源期刊
Mathematical Finance
Mathematical Finance 数学-数学跨学科应用
CiteScore
4.10
自引率
6.20%
发文量
27
审稿时长
>12 weeks
期刊介绍: Mathematical Finance seeks to publish original research articles focused on the development and application of novel mathematical and statistical methods for the analysis of financial problems. The journal welcomes contributions on new statistical methods for the analysis of financial problems. Empirical results will be appropriate to the extent that they illustrate a statistical technique, validate a model or provide insight into a financial problem. Papers whose main contribution rests on empirical results derived with standard approaches will not be considered.
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