资产定价基本定理的非交换形式

论量子模糊性与求解动态资产定价模型的潜在指数级计算加速

On Quantum Ambiguity and Potential Exponential Computational Speed-Ups to Solving Dynamic Asset Pricing Models

本文利用量子叠加与纠缠特性为动态非线性资产定价模型提出指数级加速的量子计算方案，并建立量子决策理论基础以处理模型选择中的模糊性与不确定性。

量子资产定价基本定理

Fundamental theorem for quantum asset pricing

本研究提出由量子态或密度算子描述的量子资产设定，发展了套利扩展定义，并证明了资产定价第一基本定理的量子版本，即无套利当且仅当存在使所有资产为鞅的无风险密度算子，用于量子衍生品定价。

Pricing multi-asset derivatives by finite difference method on a quantum computer

Following the recent great advance of quantum computing technology, there are growing interests in its applications to industries, including finance. In this paper, we focus on derivative pricing based on solving the Black-Scholes partial differential equation by finite difference method (FDM), which is a suitable approach for some types of derivatives but suffers from the {\it curse of dimensionality}, that is, exponential growth of complexity in the case of multiple underlying assets. We propose a quantum algorithm for FDM-based pricing of multi-asset derivative with exponential speedup with…

Quantum computational finance: martingale asset pricing for incomplete markets

A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for the model from the given asset prices, and using that probability measure to price the derivative. When the number of underlying assets and/or the number of market outcomes in the model is large, pricing can be computationally demanding. We show that a variety of quantum techniques can be applied to the pricing problem in finance, with a particular focus on i…

A highly efficient tensor network algorithm for multi-asset Fourier options pricing

Risk assessment and in particular derivatives pricing is one of the core areas in computational finance and accounts for a sizeable fraction of the global computing resources of the financial industry. We outline a quantum-inspired algorithm for multi-asset options pricing. The algorithm is based on tensor networks, which have allowed for major conceptual and numerical breakthroughs in quantum many body physics and quantum computation. In the proof-of-concept example explored, the tensor network approach yields several orders of magnitude speedup over vanilla Monte Carlo simulations. We take t…

评估量子振幅估计法在定价多资产篮子期权中的应用

Evaluating Quantum Amplitude Estimation for Pricing Multi-Asset Basket Options

本研究通过量子振幅估计法评估多资产篮子期权定价，分析不确定性量子比特与资产数量变化对精度和资源消耗的影响，探讨量子方法在金融中的可行性与局限性。