Arbitrage‐free call option surface construction using regression splines

In this work, we suggest a novel quadratic programming‐based algorithm to generate an arbitrage‐free call option surface. The empirical performance of the proposed method is evaluated using S&P 500 Index call options. Our results indicate that the proposed method provides a more precise fit to observed option prices than other alternative methodologies. Copyright © 2014 John Wiley & Sons, Ltd.     

Economic Equilibrium: Optimality and Price Decentralization

Mathematical economics has a long history and covers many interdisciplinary areas between mathematics and economics. At its center lies the theory of market equilibrium. The purpose of this expository article is to introduce mathematicians to price decentralization in general equilibrium theory. In particular, it concentrates on the role of positivity in the theory of convex economic analysis and the role of normal cones in the theory of non-convex economies.     

股票价格遵循几何分式Brown运动的期权定价

讨论了股票价格过程遵循几何分式B row n运动的欧式期权定价.由于该过程存在套利机会使得传统的期权定价方法(如资本资产定价模型(CAPM),套利定价模型(APT),动态均衡定价理论(DEPT))不可能对该期权定价.利用保险精算定价法,在对市场无其它任何假设条件下,获得了欧式期权的定价公式.并讨论了在有效期内股票支付已知红利和红利率的推广公式.     

Dynamic Strategic Pricing and Speed of Diffusion

Defining speed of diffusion as the amount of time it takes to get from one penetration level to a higher one, we introduce a dynamic model in which we study the link between pricing policy, speed of diffusion, and number of competitors in the market. Our analysis shows that, in the case of strategic (oligopolistic) competition, the speed of diffusion has an important influence on the optimal pricing policy. In particular, we find that higher speeds of diffusion create an incentive to strategically interacting firms to lower their prices.     

Optimal stopping problems by two or more decision makers: a survey

A review of the optimal stopping problem with more than a single decision maker (DM) is presented in this paper. We classify the existing literature according to the arrival of the offers, the utility of the DMs, the length of the sequence of offers, the nature of the game and the number of offers to be selected. We enumerate various definitions for this problem and describe some dynamic approaches. Fouad Ben Abdelaziz is on leave from the Institut Superieur de Gestion, University of Tunis, Tunisia e-mail: foued.benabdelaz@isg.run.tn.     

Mental representations of important real-life decisions

Two studies investigated how decision makers characterize alternatives in important real-life decisions, which they themselves had made (to leave a partner, to choose an education and to choose a home). First, the participants indicated a very high degree of involvement in the decisions studied and about half of the participants gave maximum involvement ratings for the partner decision. Second, the results showed that concepts that are essential in most decision theories, such as, consequence, probability and value were important characteristics of the decisions. Third, emotion, positive and negative affect were also important characteristics. Fourth, value and emotion were uncorrelated. Fifth, the patterns of characteristics of decisions made in the past did not differ markedly from the characteristics given to future decisions. Principal component analyses were performed on the ratings of applicability of the different characteristics across participants for each decision situation. Three factors were extracted. There was one factor for positive affect/emotions and another factor for negative affect/emotions verified in oblique solutions. Thus, different scales are needed to represent emotion/affect components (and not bipolar scales) in real-life important decisions. The third factor represented the way in which a decision was represented (moving pictures dialogue etc.). An analysis restricted to the participants who rated 100% involvement showed an additional fourth factor with “what others would think”, “similar situations”, “values” and “money” as the most prominent characteristics. This points to the importance of controlling for participant involvement in studies of human decision making to enable generalizations to real-life decisions.     

基于演化博弈的武器装备研制合同定价模型研究

针对合同的动态性，提出利用基于演化博弈建立定价模型。考虑到决策群体中个体的认识误差，对所建立的定价模型进行修正，建立带偏离的定价模型并分析了偏离对均衡解的影响。最后将以上模型应用实例进行比较分析。     

Risk-neutral valuation with infinitely many trading dates

The first Fundamental Theorem of Asset Pricing establishes the equivalence between the absence of arbitrage in financial markets and the existence of Equivalent Martingale Measures, if appropriate conditions hold. Since the theorem may fail when dealing with infinitely many trading dates, this paper draws on the A.A. Lyapunov Theorem in order to retrieve the equivalence for complete markets such that the Sharpe Ratio is adequately bounded.     

动态随机弹性在期权定价中的应用

给出动态随机弹性的概念及运算性质,讨论了动态随机弹性在期权定价模型中的应用.主要结果有:(1)在波动率为常数时,期权价格对的弹性,得到了动态随机弹性服从运动,并给出了相应的经济解释;(2)由于波动率一般不是常数,也是随机过程,因此本文进一步研究了期权价格对波动率的弹性,就股票价格的波动情况给出了数学描述和金融意义上的解释.     

标的股价服从混合过程的期权定价公式及有限元算法

本文将马尔科夫跳跃过程叠加于 Ito过程 ,形成混合过程 ,并用该过程来刻画股价走势情况。而后在标的股价服从混合过程的基础上 ,推导出了欧式看涨期权的定价公式 ,并对美式看跌期权定价给出了有限元算法。