研究了Hirst参数H>1/2分数Brown运动驱动的随机延迟微分方程(SDDE),随机积分如Duncan et al.[9]所定义的Wick-It■型随机积分,在系数具有充分正则性条件下,证明了随机延迟微分方程解的存在唯—性,其中利用了Malliavinφ-导数及随机...研究了Hirst参数H>1/2分数Brown运动驱动的随机延迟微分方程(SDDE),随机积分如Duncan et al.[9]所定义的Wick-It■型随机积分,在系数具有充分正则性条件下,证明了随机延迟微分方程解的存在唯—性,其中利用了Malliavinφ-导数及随机分析。展开更多
This paper studies the critical exercise price of American floating strike lookback options under the mixed jump-diffusion model. By using It formula and Wick-It-Skorohod integral, a new market pricing model estab...This paper studies the critical exercise price of American floating strike lookback options under the mixed jump-diffusion model. By using It formula and Wick-It-Skorohod integral, a new market pricing model established under the environment of mixed jumpdiffusion fractional Brownian motion. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given, then the American floating strike lookback options factorization formula is obtained, the results is generalized the classical Black-Scholes market pricing model.展开更多
The insurer's solvency ratio model in a class of fractional Black-Scholes markets is studied. In this market,the price of assets follows a Wick-It stochastic differential equation,which is driven by the fraction...The insurer's solvency ratio model in a class of fractional Black-Scholes markets is studied. In this market,the price of assets follows a Wick-It stochastic differential equation,which is driven by the fractional Brownian motion. The market coefficients of market model are deterministic functions. By the stochastic calculus of the fractional Brownian motion and the pricing formula of European call option for the fractional Brownian motion,the explicit formula for the expected present value of shareholder's terminal payoff is given. The model extends the existing results.展开更多
In order to price European contingent claim in a class of fractional Black-Scholes market,where the prices of assets follow a Wick-It stochastic differential equation driven by the fractional Brownian motion and mar...In order to price European contingent claim in a class of fractional Black-Scholes market,where the prices of assets follow a Wick-It stochastic differential equation driven by the fractional Brownian motion and market coefficients are deterministic functions,the pricing formula of European call option was explicitly derived by the method of the stochastic calculus of the fractional Brownian motion.A result about fractional Clark derivative was also obtained.展开更多
基金Supported by the Fundamental Research Funds of Lanzhou University of Finance and Economics(Lzufe2017C-09)
文摘This paper studies the critical exercise price of American floating strike lookback options under the mixed jump-diffusion model. By using It formula and Wick-It-Skorohod integral, a new market pricing model established under the environment of mixed jumpdiffusion fractional Brownian motion. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given, then the American floating strike lookback options factorization formula is obtained, the results is generalized the classical Black-Scholes market pricing model.
基金National Natural Science Foundations of China(Nos.71271003,71571001,11326121)Natural Science Foundation of Anhui Province,China(No.1608085M A02)+1 种基金Teaching Research Project of Anhui Province,China(No.2013jyxm111)Opening Project of Financial Engineering Research and Development Center of Anhui Polytechnic University,China(No.JRGCKF201502)
文摘The insurer's solvency ratio model in a class of fractional Black-Scholes markets is studied. In this market,the price of assets follows a Wick-It stochastic differential equation,which is driven by the fractional Brownian motion. The market coefficients of market model are deterministic functions. By the stochastic calculus of the fractional Brownian motion and the pricing formula of European call option for the fractional Brownian motion,the explicit formula for the expected present value of shareholder's terminal payoff is given. The model extends the existing results.
基金National Natural Science Foundation of China(No.10826098)Natural Science Foundation of Anhui Province,China(No.090416225)Anhui Natural Science Foundation of Universities,China(No.KJ2010A037)
文摘In order to price European contingent claim in a class of fractional Black-Scholes market,where the prices of assets follow a Wick-It stochastic differential equation driven by the fractional Brownian motion and market coefficients are deterministic functions,the pricing formula of European call option was explicitly derived by the method of the stochastic calculus of the fractional Brownian motion.A result about fractional Clark derivative was also obtained.