英文标题：
《Dynamic Conic Finance via Backward Stochastic Difference Equations》
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作者：
Tomasz R. Bielecki, Igor Cialenco and Tao Chen
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最新提交年份：
2014
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英文摘要：
  We present an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities in a discrete time setup using theory of dynamic acceptability indices. In the first part of the paper we develop the theory of dynamic subscale invariant performance measures, on a general probability space, and discrete time setup. We prove a representation theorem of such measures in terms of a family of dynamic convex risk measures, and provide a representation of dynamic risk measures in terms of g-expectations, and solutions of BS$\\Delta$Es with convex drivers. We study the existence and uniqueness of the solutions, and derive a comparison theorem for corresponding BS$\\Delta$Es.   In the second part of the paper we discuss a market model for dividend paying securities by introducing the pricing operators that are defined in terms of dynamic acceptability indices, and find various properties of these operators. Using these pricing operators, we define the bid and ask prices for the underlying securities and then for derivatives in this market. We show that the obtained market model is arbitrage free, and we also prove a series of properties of these prices.
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中文摘要：
我们提出了一个无套利的理论框架，利用动态可接受性指数理论，在离散时间系统中对股息支付证券的买入和卖出价格进行建模。在本文的第一部分，我们发展了一般概率空间上的动态子尺度不变性能度量理论和离散时间设置。我们用一系列动态凸风险测度证明了这类测度的一个表示定理，并用g-期望给出了动态风险测度的一个表示，以及带凸驱动的BS$\\Delta$Es的解。我们研究了解的存在性和唯一性，并导出了相应的BS$\\Delta$Es的一个比较定理。在本文的第二部分中，我们通过引入由动态可接受性指数定义的定价算子，讨论了分红证券的市场模型，并找到了这些算子的各种性质。使用这些定价操作符，我们定义了标的证券的买入价和卖出价，然后定义了该市场中衍生产品的买入价和卖出价。我们证明了所得到的市场模型是无套利的，并且证明了这些价格的一系列性质。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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