BOUNDARY LAYER ESTIMATION OF A SINGULAR PROBLEM WITH LIMIT EQUATION OF ORDER 2

ＢＯＵＮＤＡＲＹＬＡＹＥＲＥＳＴＩＭＡＴＩＯＮＯＦＡＳＩＮＧＵＬＡＲＰＲＯＢＬＥＭＷＩＴＨＬＩＭＩＴＥＱＵＡＴＩＯＮＯＦＯＲＤＥＲ２ＨＥＣＨＥＮＧ（何成）ＺＨＡＮＧＷＥＩＴＡＯ（张维弢）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，Ｃｈｉｎｅ...     

THE RADICALS OF HOPF MODULE ALGEBRAS

ＴＨＥＲＡＤＩＣＡＬＳＯＦＨＯＰＦＭＯＤＵＬＥＡＬＧＥＢＲＡＳＺＨＡＮＧＳＨＯＵＣＨＵＡＮ＊ＡｂｓｔｒａｃｔＴｈｅｃｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆＨ－ｐｒｉｍｅｒａｄｉｃａｌｉｓｇｉｖｅｎｉｎｍａｎｙｗａｙｓ．Ｍｅａｎｔｉｍｅ，ｔｈｅｒｅｌａｔｉ...     

SOURCE－TYPE SOLUTIONS OF A QUASILINEAR DEGENERATE PARABOLIC EQUATION WITH ABSORPTION

ＳＯＵＲＣＥ－ＴＹＰＥ ＳＯＬＵＴＩＯＮＳ ＯＦ Ａ ＱＵＡＳＩＬＩＮＥＡＲ ＤＥＧＥＮＥＲＡＴＥ ＰＡＲＡＢＯＬＩＣ ＥＱＵＡＴＩＯＮ ＷＩＴＨ ＡＢＳＯＲＰＴＩＯＮ￥ＺＨＡＯＪＵＮＮＩＮＧＡｂｓｔｒａｃｔ：Ｔｈｅｅｘｉｓｔｅｎｃｅａｎｄｎｏｎｅｘ...     

COMPARISON THEOREMS TO BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

ＣＯＭＰＡＲＩＳＯＮＴＨＥＯＲＥＭＳＴＯＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＬＩＹＯＮＧ；ＷＡＮＧＨＵＡＩＺＨＯＮＧＡｂｓｔｒａｃｔ：Ａｕｎｉｆｉｅｄａｐｐｒｏａｃｈｉｓｇｉｖｅ...     

ON THE BOUNDED AND UNBOUNDED SOLUTIONS OF ONE DIMENSIONAL NONLINEAR REACTION－DIFFUSION PROBLEM

ＯＮＴＨＥＢＯＵＮＤＥＤＡＮＤＵＮＢＯＵＮＤＥＤＳＯＬＵＴＩＯＮＳＯＦＯＮＥＤＩＭＥＮＳＩＯＮＡＬＮＯＮＬＩＮＥＡＲＲＥＡＣＴＩＯＮ－ＤＩＦＦＵＳＩＯＮＰＲＯＢＬＥＭ￥ＧＥＷＥＩＧＡＯＲ．Ｏ．ＷＥＢＥＲＡｂｓｔｒａｃｔ：Ｔｈｅｅｘｉｓｔｅｎｃｅｏｆｂ...     

INITIAL BOUNDARY VALUE PROBLEMS FOR PARABOLIC EQUATIONS IN LIPSCHITZ CYLINDERS

ＩＮＩＴＩＡＬ ＢＯＵＮＤＡＲＹ ＶＡＬＵＥ ＰＲＯＢＬＥＭＳ ＦＯＲ ＰＡＲＡＢＯＬＩＣ ＥＱＵＡＴＩＯＮＳ ＩＮ ＬＩＰＳＣＨＩＴＺ ＣＹＬＩＮＤＥＲＳ ￥ＧＡＯＷＥＮＪＩＥＡｂｓｔｒａｃｔ：Ｔｈｅｉｎｉｔｉａｌ－Ｄｉｒｉｃｈｌｅｔａｎｄｉｎｉｔ...     

A modified Frank-Wolfe algorithm and its convergence properties

ＡＭＯＤＩＦＩＥＤＦＲＡＮＫ－ＷＯＬＦＥＡＬＧＯＲＩＴＨＭＡＮＤＩＴＳＣＯＮＶＥＲＧＥＮＣＥＰＲＯＰＥＲＴＩＥＳＷＵＦＡＮＧ（吴方）ＷＵＳＨＩＱＵＡＮ（吴士泉）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ,ｔｈｅＣｈｉｎｅｓｅＡｃａｄ...     

SOLUTIONS CONTAINING DELTA－WAVES OF CAUCHY PROBLEMS FOR A NONSTRICTLY HYPERBOLIC SYSTEM

ＳＯＬＵＴＩＯＮＳＣＯＮＴＡＩＮＩＮＧＤＥＬＴＡ－ＷＡＶＥＳＯＦＣＡＵＣＨＹＰＲＯＢＬＥＭＳＦＯＲＡＮＯＮＳＴＲＩＣＴＬＹＨＹＰＥＲＢＯＬＩＣＳＹＳＴＥＭ￥ＨＵＡＮＧＦＥＩＭＩＮ（黄飞敏）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ,Ｓｈａｎｔｏｕ...     

GLOBAL CONVERCENCE OF THE FLETCHER-REEVES ALGORITHM WITH INEXACT LINESEARCH

ＧＬＯＢＡＬＣＯＮＶＥＲＣＥＮＣＥＯＦＴＨＥＦＬＥＴＣＨＥＲ－ＲＥＥＶＥＳＡＬＧＯＲＩＴＨＭＷＩＴＨＩＮＥＸＡＣＴＬＩＮＥＳＥＡＲＣＨ￥ＬＩＵＧＵＡＮＧＨＵＩ；ＨＡＮＪＩＹＥ；ＡＮＤＹＩＮＨＯＮＧＸＩＡＡｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｉ...     

RANDOM ITERAtION OF HOLOMORPHIC SELF-MAPS OVER BOUNDED DOMAINS IN C~N

ＲＡＮＤＯＭＩＴＥＲＡＴＩＯＮＯＦＨＯＬＯＭＯＲＰＨＩＣＳＥＬＦ－ＭＡＰＳＯＶＥＲＢＯＵＮＤＥＤＤＯＭＡＩＮＳＩＮＣ~Ｎ￥ＺＨＡＮＧＷＥＮＪＵＮ；ＲＥＮＦＵＹＡＯ（ＤｅｐａｒａｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｅｎａｌＵｎｉｖｅｒｓｉｔｙｔＫａ?..     

A BLACK-SCHOLES FORMULA FOR OPTION PRICING WITH DIVIDENDS

Abstract. We obtain a Black-Scholes formula for the arbitrage-free pricing of Eu-ropean Call options with constant coefficients when the underlylng stock generatesdividends. To hedge the Call option, we will always borrow money from bank. We seethe influence of the dividend term on the option pricing via the comparison theoremof BSDE(backward stochastic di~erential equation [5], [7]). We also consider the option pricing problem in terms of the borrowing rate R whichis not equal to the interest rate r. The corresponding Black-Sdxoles formula is given.We notice that it is in fact the borrowing rate that plays the role in the pricing formula.     

Richter’s local limit theorem and Black–Scholes type formulas

We prove a Black–Scholes type formula when the geometric Brownian motion originates from approximations by multinomial distributions. It is shown that the variance appearing in the Black–Scholes formula for option pricing can be structured according to occurrences of different types of events at each time instance using a local limit theorem for multinomial distributions in Richter (1956). The general approach has first been developed in Kan (2005).     

Wick–Itô formula for regular processes and applications to the Black and Scholes formula

We derive a Wick–Itô formula, that is, an Itô-type formula based on Wick integration. We derive it in the context of regular Gaussian processes which include Brownian motion and fractional Brownian motion with Hurst parameter greater than 1/2. We then consider applications to the Black and Scholes formula for the pricing of a European call option. It has been shown that using Wick integration in this context is problematic for economic reasons. We show that it is also problematic for mathematical reasons because the resulting Black and Scholes formula depends only on the variance of the process and not on its dependence structure.     

具有变系数和红利的多维Black-Scholes模型

本文提出具有变系数和红利的多维Ｂｌａｃｈ－Ｓｃｈｏｌｅｓ模型,利用倒向随机微分方程和鞅方法,得到欧式未定权益的一般定价公式及套期保值策略,在具体金融市场,给出欧式期权的定价公式和套期保值策略,以及美式看涨期权价格的界。     

Option pricing for a logstable asset price model

The paper generalises the celebrated Black and Scholes [1] European option pricing formula for a class of logstable asset price models. The theoretical option prices have the potential to explain the implied volatility smiles evident in the market.     

简单可转换债券的定价——一种鞅方法

可转换债券作为债券和期权的混合体,其定价比债券和期权的定价都要复杂.本文用鞅方法讨论可转换债券的定价问题,给出了便于计算的类似于Black-Scholes模型的定价公式.但我们利用鞅方法使定价模型的推导更自然.基于这一定价模型,可转换债券的价格可分解为转换期权的价格和简单债券的价值之和.     

Call option pricing and replication under economic friction

In this paper we incorporate multiple transactions costs in the option pricing formula of Black and Scholes (1972). The effect of introducing economic friction in the equilibrium equation is studied and summarized in some central propositions. The analysis provides part of the results needed for capturing the economic effects of transactions costs in the pricing process.     

连续SV模型下衍生证券定价

1973年 Black- Scholes公式的出现极大推动衍生证券的发展 ,该公式的不足是假设影响标的资产价格波动的扩散系数为常数 ;80年代后期的 SV模型是针对该问题的离散统计模型。本文在两者的基础上讨论SV模型和 Black- Scholes公式结合。在讨论一般化衍生证券定价的基础上 ,通过 SV模型的连续化 ,构造一个2维随机微分方程 ,最后讨论了一种可以接受的数值计算方法     

Risk Minimizing Option Pricing in a Regime Switching Market

Abstract

We study option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of a stock depends on a finite state Markov chain. Using a minimal martingale measure we show that the risk minimizing option price satisfies a system of Black–Scholes partial differential equations with weak coupling.     

Bachelier model with stopping time and its insurance application

A modification of a classical Bachelier model by letting a stock price absorb at zero is revisited. Alternative proofs are given to derive option pricing formulas under the modified Bachelier model and numerical comparison with the Black–Scholes formula is provided. Quantile hedging methodology is developed for both classical and modified Bachelier models and application to pricing the pure endowment with fixed guarantee life insurance contracts is demonstrated, both theoretically and by means of a numerical example.