A comprehensive mathematical approach to exotic option pricing

This work illustrates how several new pricing expressions for exotic options can be derived within a Lévy framework by employing a unique pricing expression. To the purpose, a unifying formula is obtained by solving some nested Cauchy problem for pseudodifferential equations generalizing Black–Scholes PDE. The main result extends (Agliardi R. The quintessential option pricing formula under Lévy processes. Applied Mathematics Letters 2009; 22:1626‐1631) and is a powerful tool for generating new valuation expressions. Several examples of pricing formulas under the Lévy processes are provided to illustrate the flexibility of the method. Some of them are new in the financial literature. Finally, many existing pricing formulas of the traditional Gaussian model are easily obtained as a by‐product. Copyright © 2012 John Wiley & Sons, Ltd.     

A new look at the role of players’ weights in the weighted Shapley value

everal new families of semivalues for weighted n-person transferable utility games are axiomatically constructed and discussed under increasing collections of axioms, where the weighted Shapley value arises as the resulting one member family. A more general approach to such weighted games defined in the form of two components, a weight vector λ and a classical TU-game v, is provided. The proposed axiomatizations are done both in terms of λ and v. Several new axioms related to the weight vector λ are discussed, including the so-called “amalgamating payoffs” axiom, which characterizes the value of a weighted game in terms of another game with a smaller number of players. They allow for a new look at the role of players’ weights in the context of the weighted Shapley value for the model of weighted games, giving new properties of it. Besides, another simple formula for the weighted Shapley value is found and examples illustrating some surprising behavior of it in the context of players’ weights are given. The paper contains a wide discussion of the results obtained.     

A uniform asymptotic expansion for stochastic volatility model in pricing multi‐asset European options

In this paper, we consider a stochastic volatility model for pricing multi‐asset European options that are widely used in the real world, under the assumption that the volatilities are driven by different OU processes. Using the singular perturbation method for multi‐parameter and the boundary layer theory, we derive a uniform asymptotic expansion for the option prices, as well as the uniform error estimates. Copyright © 2011 John Wiley & Sons, Ltd.     

科技成果转化团队知识网络中知识共享的博弈模型

构建了科技成果转化团队知识网络中知识共享的演化博弈模型,分析了核心节点的收益分配策略和普通节点的知识共享策略选择决策,得到了模型的均衡解、复制动态和稳定性,讨论了知识共享的影响因素,并进行了数值实验.研究结果表明:1)核心节点选择"高收益分配策略"、普通节点选择"知识共享策略"的概率是一个震荡性螺旋提升过程;2)影响普通节点知识共享的正向因素有"普通节点用于知识共享的资金投入量"等;3)影响核心节点收益分配策略选择的正向因素有"普通节点出入度期望值"等.     

几何平均下的水平重置期权定价

针对重置期权的风险对冲△跳现象,研究了一种亚式特征的水平重置期权的定价问题.首先在BS模型下用股票的几何平均价格作为水平重置期权执行价格重置与否的统计量,然后运用测度变换和鞅定价方法得到了风险中性定价公式,最后利用风险中性定价公式得出风险对冲△值的显示解,改进了水平重置期权的部分已有结果.     

分形布朗运动下有交易成本的外汇期权定价

研究了有交易成本的分形Black-Scholes外汇期权定价问题.基于汇率的分形布朗运动分布假设,运用分形布朗运动的性质和随机微积分方法,得到了欧式外汇期权价格所满足的偏微分方程.最后,建立离散时间条件下的非线性期权定价模型,并且通过解期权价格的偏微分方程给出了有交易成本的欧式外汇期权定价公式.     

全球化背景下核型创新网络竞争机制研究——基于改进LV-EG模型的仿真分析

在全球化背景下,核型创新网络在向全球创新网络演进的过程中面临多市场竞争和关键资源竞争的双重考验。首先构建全球市场环境下核型创新网络多层次竞合模型;其次,运用Lotka-Volterra模型和演化博弈模型分别剖析核心企业间的竞争关系和尾端企业间的竞合关系,并据此构建改进的LV-EG模型以分析尾端企业竞合关系对核心企业间竞争关系的作用机理;最后,运用matlab对改进的LV-EG模型进行仿真。仿真结果表明:核心企业的尾端企业报酬支付能力、创新产品生产能力、创新环境和网络结构对核型创新网络在全球范围内吸引优质企业并在全球市场环境中获取竞争优势具有重要影响。     

区域性物流园区竞合策略的演化博弈分析

针对我国物流园区发展现状,探讨了区域性物流园区之间的竞合策略。建立了区域性物流园区竞合策略的演化博弈模型,据此分析了物流园区间竞争合作关系演变发展的趋势。研究表明,区域性物流园区之间长期竞争合作演化的结果是完全竞争或完全合作;在一定条件下,物流园区竞合策略选择的动态演化过程收敛于哪一个均衡点受到博弈发生的初始状态的影响,演化的路径和最终状态与转化能力、风险水平以及资源水平密切相关。     

二级供应链上不完美互补产品的定价决策

建立一个由两个制造商和一个零售商组成供应链模型,以求解制造商和零售商的最优定价决策,其中两个制造商向零售商批发的产品是不完美互补的,且零售商采取混合捆绑策略销售这两种产品。考虑三种情形下的决策:(1)完全非合作博弈;(2)局部合作博弈;(3)合作博弈。通过比较前两种情形下的决策,利用Nash协商模型求解得到消除水平和垂直供应链冲突的最优定价决策。与完全非合作博弈决策相比,局部合作博弈决策对制造商是有利的,在一定的条件下也可以实现对零售商收益的帕累托改进;而合作博弈决策在任何情况下都要明显地优于完全非合作博弈决策以及局部合作博弈决策,同时合作博弈决策下的最优产品需求量相比局部合作博弈决策下的最优产品需求量提高了一倍。最后,通过数值试验验证了文章所得结论。     

负债代理冲突下企业投融资互动行为的实物期权分析

准确分析企业投融资之间的互动关系,实现两种决策的协同,有助于提高企业决策效率和项目价值.通过把项目融资政策内生到投资决策的实物期权模型中,构建基于股东价值最大化和企业价值最大化的投融资决策互动模型,得到两种情形下的投融资决策临界点和期权价值,并借助数值分析负债代理冲突对企业投融资行为的影响.研究结果表明,负债融资既可能引发过度投资问题,也可能抑制投资.这种非效率投资将相应地提高负债融资的成本,对企业的负债融资产生抑制作用.