论文标题
连续融资的无模型方法
A model-free approach to continuous-time finance
论文作者
论文摘要
我们提出了一种基于因果函数演算的非稳态，路径方向的方法。我们介绍了一个自我融资的定义，没有任何集成概念，并表明自发投资组合的价值是路径的积分（每个自我融资策略都是梯度），并且功能计算的通用域本质上是无套的。然后，我们考虑在一组通用方案中获得路径依赖性收益的问题。我们在差异游戏中应用以撒的过渡原理，并获得最佳解决方案的验证定理，该定理以完全非线性路径依赖性方程为特征。对于亚洲选项，我们获得明确的解决方案。
We present a non-probabilistic, pathwise approach to continuous-time finance based on causal functional calculus. We introduce a definition of self-financing, free from any integration concept and show that the value of a self-financing portfolio is a pathwise integral (every self-financing strategy is a gradient) and that generic domain of functional calculus is inherently arbitrage-free. We then consider the problem of hedging a path-dependent payoff across a generic set of scenarios. We apply the transition principle of Isaacs in differential games and obtain a verification theorem for the optimal solution, which is characterised by a fully non-linear path-dependent equation. For the Asian option, we obtain explicit solution.
