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摘要翻译：
本文发展了一类新的金融市场模型。这些模型是基于广义电报过程：具有交替速度的马尔可夫随机流和在速度切换时发生的跳跃。虽然这类市场可能会有套利机会，但如果股票价格的跳跃方向与其速度和利率行为有一定的对应关系，则所考虑的模型是无套利和完全的。推导了Black-Scholes基本微分方程的一个模拟，但与Black-Scholes模型相反，该方程是双曲型的。利用完全套期保值和分位数套期保值，得到了欧式期权价格的显式公式。
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英文标题：
《On Financial Markets Based on Telegraph Processes》
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作者：
Nikita Ratanov, Alexander Melnikov
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最新提交年份：
2007
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
The paper develops a new class of financial market models. These models are based on generalized telegraph processes: Markov random flows with alternating velocities and jumps occurring when the velocities are switching. While such markets may admit an arbitrage opportunity, the model under consideration is arbitrage-free and complete if directions of jumps in stock prices are in a certain correspondence with their velocity and interest rate behaviour. An analog of the Black-Scholes fundamental differential equation is derived, but, in contrast with the Black-Scholes model, this equation is hyperbolic. Explicit formulas for prices of European options are obtained using perfect and quantile hedging.
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PDF链接：
https://arxiv.org/pdf/0712.3428
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