论文标题
量子资产定价的基本定理
Fundamental theorem for quantum asset pricing
论文作者
论文摘要
量子计算机有可能通过使用量子估计来为财务定价问题提供优势。在更广泛的背景下，可以合理询问市场和市场本身具有量子财产的情况。在这项工作中，我们考虑了一种财务环境，在这种情况下，而不是通过经典概率，而是由纯量子状态或更一般而言的量子密度运算符描述。这种设置自然会导致新的资产类别，我们称之为量子资产。在假设此类资产具有价格并且可以交易的假设下，我们开发了套利的扩展定义，以量化没有相应风险的收益。我们的主要结果是资产定价的第一个基本定理的量子版本。如果并且仅在没有套利的情况下，就存在所有资产均为marting的无风险密度操作员。该密度运算符用于量子衍生物的定价。为了证明定理，我们研究了radon-Nikodym测量变化的密度操作员版本。我们提供的例子来说明理论。
Quantum computers have the potential to provide an advantage for financial pricing problems by the use of quantum estimation. In a broader context, it is reasonable to ask about situations where the market and the assets traded on the market themselves have quantum properties. In this work, we consider a financial setting where instead of by classical probabilities the market is described by a pure quantum state or, more generally, a quantum density operator. This setting naturally leads to a new asset class, which we call quantum assets. Under the assumption that such assets have a price and can be traded, we develop an extended definition of arbitrage to quantify gains without the corresponding risk. Our main result is a quantum version of the first fundamental theorem of asset pricing. If and only if there is no arbitrage, there exists a risk-free density operator under which all assets are martingales. This density operator is used for the pricing of quantum derivatives. To prove the theorem, we study the density operator version of the Radon-Nikodym measure change. We provide examples to illustrate the theory.
