英文标题：
《Calibration of Local-Stochastic Volatility Models by Optimal Transport》
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作者：
Ivan Guo, Gregoire Loeper, Shiyi Wang
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最新提交年份：
2021
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英文摘要：
  In this paper, we study a semi-martingale optimal transport problem and its application to the calibration of Local-Stochastic Volatility (LSV) models. Rather than considering the classical constraints on marginal distributions at initial and final time, we optimise our cost function given the prices of a finite number of European options. We formulate the problem as a convex optimisation problem, for which we provide a PDE formulation along with its dual counterpart. Then we solve numerically the dual problem, which involves a fully non-linear Hamilton-Jacobi-Bellman equation. The method is tested by calibrating a Heston-like LSV model with simulated data and foreign exchange market data.
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中文摘要：
本文研究了一个半鞅最优运输问题及其在局部随机波动率（LSV）模型标定中的应用。考虑到有限数量的欧式期权的价格，我们优化了成本函数，而不是考虑初始和最终阶段边际分布的经典约束。我们将该问题描述为一个凸优化问题，为此我们提供了一个PDE公式及其对偶形式。然后，我们数值求解对偶问题，该问题涉及一个完全非线性的Hamilton-Jacobi-Bellman方程。通过用模拟数据和外汇市场数据校准一个类似赫斯顿的LSV模型，对该方法进行了检验。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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