Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of Europ...Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.展开更多
This paper studies the multi-dimensional Black-Scholes model of security valnation. The extension of the Black-Scholes model implies; the partial differential equation derived from an absence of arbitrage which the au...This paper studies the multi-dimensional Black-Scholes model of security valnation. The extension of the Black-Scholes model implies; the partial differential equation derived from an absence of arbitrage which the authors solve by using the Feynmeu-Kac Formula. Then they compute its special example by solving the multi-variable partial differential equation.展开更多
In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging e...In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging.展开更多
Based on the analog between the stochastic dynamics and quantum harmonic oscillator,we propose a market force driving model to generalize the Black-Scholes model in finance market.We give new schemes of option pricing...Based on the analog between the stochastic dynamics and quantum harmonic oscillator,we propose a market force driving model to generalize the Black-Scholes model in finance market.We give new schemes of option pricing,in which we can take various unexpected market behaviors into account to modify the option pricing.As examples,we present several market forces to analyze their effects on the option pricing.These results provide us two practical applications.One is to be used as a new scheme of option pricing when we can predict some hidden market forces or behaviors emerging.The other implies the existence of some risk premium when some unexpected forces emerge.展开更多
We consider an economic model with a deterministic money market account and a finite set of basic economic risks. The real-world prices of the risks are represented by continuous time stochastic processes satisfying a...We consider an economic model with a deterministic money market account and a finite set of basic economic risks. The real-world prices of the risks are represented by continuous time stochastic processes satisfying a stochastic differential equation of diffusion type. For the simple class of log-normally distributed instantaneous rates of return, we construct an explicit state-price deflator. Since this includes the Black-Scholes and the Vasicek (Ornstein-Uhlenbeck) return models, the considered deflator is called Black-Scholes- Vasicek deflator. Besides a new elementary proof of the Black-Scholes and Margrabe option pricing formulas a validation of these in a multiple risk economy is achieved.展开更多
In this paper,a two dimensional(2D)fractional Black-Scholes(FBS)model on two assets following independent geometric Lévy processes is solved numerically.A high order convergent implicit difference scheme is const...In this paper,a two dimensional(2D)fractional Black-Scholes(FBS)model on two assets following independent geometric Lévy processes is solved numerically.A high order convergent implicit difference scheme is constructed and detailed numerical analysis is established.The fractional derivative is a quasidifferential operator,whose nonlocal nature yields a dense lower Hessenberg block coefficient matrix.In order to speed up calculation and save storage space,a fast bi-conjugate gradient stabilized(FBi-CGSTAB)method is proposed to solve the resultant linear system.Finally,one example with a known exact solution is provided to assess the effectiveness and efficiency of the presented fast numerical technique.The pricing of a European Call-on-Min option is showed in the other example,in which the influence of fractional derivative order and volatility on the 2D FBS model is revealed by comparing with the classical 2D B-S model.展开更多
The properties of N = 7, 8, 9 isotones with Z = 4 - 8 are studied in the framework of the single-particle shell model. A tentative orbit-orbit coupling is introduced in the average nuclear potential. Calculations give...The properties of N = 7, 8, 9 isotones with Z = 4 - 8 are studied in the framework of the single-particle shell model. A tentative orbit-orbit coupling is introduced in the average nuclear potential. Calculations give a unified description of the structures of N- 7, 8, 9 isotones. The neutron level inversion in N = 7 and N = 9 isotones is discussed. The ground-state level inversion in 11Be and ^15C is reproduced. The inversion between 2s1/2 and 1d5/2 neutron levels in 14B and 13Be is predicted. The possible halo structures in N = 7 and N = 9 isotones are analysed. The numerical results confirm the one-neutron halo structures in ^11Be（2s1/2）, ^11 Be（1p1/2）, ^12B（2s1/2）, ^133C（2s1/2）, ^14B（2s1/2） and ^15C（2s1/2）. The study implies that the attempt of considering orbit orbit interaction in the shell model may be a feasible way to explain the anomalous properties of exotic light nuclei.展开更多
Similar to the method of continuum mechanics, the variation of the price of index futures is viewed to be continuous and regular. According to the characteristic of index futures, a basic equation of price of index fu...Similar to the method of continuum mechanics, the variation of the price of index futures is viewed to be continuous and regular. According to the characteristic of index futures, a basic equation of price of index futures was established. It is a differential equation, its solution shows that the relation between time and price forms a logarithmic circle. If the time is thought of as the probability of its corresponding price, then such a relation is perfectly coincided with the main assumption of the famous formula of option pricing, based on statistical theory, established by Black and Scholes winner of 1997 Nobel' prize on economy. In that formula, the probability of price of basic assets (they stand for index futures here) is assummed to be a logarithmic normal distribution. This agreement shows that the same result may be obtained by two analytic methods with different bases. However, the result, given by assumption by Black-Scholes, is derived from the solution of the differential equation.展开更多
Rheumatoid arthritis (RA) is an immune-mediated chronic inflammatory disease that causes huge destruction to human body. IL1B encodes key mediator IL-1β protein, which plays an important role in the pathogenesis of i...Rheumatoid arthritis (RA) is an immune-mediated chronic inflammatory disease that causes huge destruction to human body. IL1B encodes key mediator IL-1β protein, which plays an important role in the pathogenesis of inflammatory syndromes. The aim of this study was to evaluate the association between IL1B polymorphisms and RA. A meta-analysis was performed on the association between three IL1B polymorphisms (IL1B-31: rs1143627;IL1B-511: rs16944;IL1B + 3954: rs1143634) and RA. A trend of significant association was observed between IL1B + 3954 and RA (p = 0.06, odd ratio (OR) = 1.19, 95% confidential interval (CI) = 1.00-1.42). A significant association was found in Europeans under the dominant model between IL1B-511T and RA (p = 0.03, OR = 0.89, 95% CI = 0.81-0.99). Our meta-analysis indicated that IL1B ? 511-T played a protective role against RA in Europeans, and that IL1B + 3954-T had the potential to increase the risk of RA. Future large-scale studies should be considered to confirm the association between IL1B polymorphisms and RA.展开更多
In this paper, we consider the problem to determine the optimal time to sell an asset that its price conforms to the Black-Schole model but its drift is a discrete random variable taking one of two given values and th...In this paper, we consider the problem to determine the optimal time to sell an asset that its price conforms to the Black-Schole model but its drift is a discrete random variable taking one of two given values and this probability distribution behavior changes chronologically. The result of finding the optimal strategy to sell the asset is the first time asset price falling into deterministic time-dependent boundary. Moreover, the boundary is represented by an increasing and continuous monotone function satisfying a nonlinear integral equation. We also conduct to find the empirical optimization boundary and simulate the asset price process.展开更多
Under the assumption of the underlying asset is driven by the mixed fractional Brownian motion, we obtain the mixed fractionalBlack-Scholes partial differential equation by fractional Ito formula, and the pricing form...Under the assumption of the underlying asset is driven by the mixed fractional Brownian motion, we obtain the mixed fractionalBlack-Scholes partial differential equation by fractional Ito formula, and the pricing formula of perpetual American put option bythis partial differential equation theory.展开更多
文摘Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.
文摘This paper studies the multi-dimensional Black-Scholes model of security valnation. The extension of the Black-Scholes model implies; the partial differential equation derived from an absence of arbitrage which the authors solve by using the Feynmeu-Kac Formula. Then they compute its special example by solving the multi-variable partial differential equation.
基金Supported by the National Natural Science Foundation of China(11671115)the Natural Science Foundation of Zhejiang Province(LY14A010025)
文摘In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging.
文摘Based on the analog between the stochastic dynamics and quantum harmonic oscillator,we propose a market force driving model to generalize the Black-Scholes model in finance market.We give new schemes of option pricing,in which we can take various unexpected market behaviors into account to modify the option pricing.As examples,we present several market forces to analyze their effects on the option pricing.These results provide us two practical applications.One is to be used as a new scheme of option pricing when we can predict some hidden market forces or behaviors emerging.The other implies the existence of some risk premium when some unexpected forces emerge.
文摘We consider an economic model with a deterministic money market account and a finite set of basic economic risks. The real-world prices of the risks are represented by continuous time stochastic processes satisfying a stochastic differential equation of diffusion type. For the simple class of log-normally distributed instantaneous rates of return, we construct an explicit state-price deflator. Since this includes the Black-Scholes and the Vasicek (Ornstein-Uhlenbeck) return models, the considered deflator is called Black-Scholes- Vasicek deflator. Besides a new elementary proof of the Black-Scholes and Margrabe option pricing formulas a validation of these in a multiple risk economy is achieved.
基金supported by the Natural Science Foundation of Fujian Province2017J01555,2017J01502,2017J01557 and 2019J01646the National NSF of China 11201077+1 种基金China Scholarship Fundthe Natural Science Foundation of Fujian Provincial Department of Education JAT160274
文摘In this paper,a two dimensional(2D)fractional Black-Scholes(FBS)model on two assets following independent geometric Lévy processes is solved numerically.A high order convergent implicit difference scheme is constructed and detailed numerical analysis is established.The fractional derivative is a quasidifferential operator,whose nonlocal nature yields a dense lower Hessenberg block coefficient matrix.In order to speed up calculation and save storage space,a fast bi-conjugate gradient stabilized(FBi-CGSTAB)method is proposed to solve the resultant linear system.Finally,one example with a known exact solution is provided to assess the effectiveness and efficiency of the presented fast numerical technique.The pricing of a European Call-on-Min option is showed in the other example,in which the influence of fractional derivative order and volatility on the 2D FBS model is revealed by comparing with the classical 2D B-S model.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10125521 and 10535010, and the National Major State Basic Research and Development Programme of China under Grant No C2000077400.
文摘The properties of N = 7, 8, 9 isotones with Z = 4 - 8 are studied in the framework of the single-particle shell model. A tentative orbit-orbit coupling is introduced in the average nuclear potential. Calculations give a unified description of the structures of N- 7, 8, 9 isotones. The neutron level inversion in N = 7 and N = 9 isotones is discussed. The ground-state level inversion in 11Be and ^15C is reproduced. The inversion between 2s1/2 and 1d5/2 neutron levels in 14B and 13Be is predicted. The possible halo structures in N = 7 and N = 9 isotones are analysed. The numerical results confirm the one-neutron halo structures in ^11Be（2s1/2）, ^11 Be（1p1/2）, ^12B（2s1/2）, ^133C（2s1/2）, ^14B（2s1/2） and ^15C（2s1/2）. The study implies that the attempt of considering orbit orbit interaction in the shell model may be a feasible way to explain the anomalous properties of exotic light nuclei.
文摘Similar to the method of continuum mechanics, the variation of the price of index futures is viewed to be continuous and regular. According to the characteristic of index futures, a basic equation of price of index futures was established. It is a differential equation, its solution shows that the relation between time and price forms a logarithmic circle. If the time is thought of as the probability of its corresponding price, then such a relation is perfectly coincided with the main assumption of the famous formula of option pricing, based on statistical theory, established by Black and Scholes winner of 1997 Nobel' prize on economy. In that formula, the probability of price of basic assets (they stand for index futures here) is assummed to be a logarithmic normal distribution. This agreement shows that the same result may be obtained by two analytic methods with different bases. However, the result, given by assumption by Black-Scholes, is derived from the solution of the differential equation.
文摘Rheumatoid arthritis (RA) is an immune-mediated chronic inflammatory disease that causes huge destruction to human body. IL1B encodes key mediator IL-1β protein, which plays an important role in the pathogenesis of inflammatory syndromes. The aim of this study was to evaluate the association between IL1B polymorphisms and RA. A meta-analysis was performed on the association between three IL1B polymorphisms (IL1B-31: rs1143627;IL1B-511: rs16944;IL1B + 3954: rs1143634) and RA. A trend of significant association was observed between IL1B + 3954 and RA (p = 0.06, odd ratio (OR) = 1.19, 95% confidential interval (CI) = 1.00-1.42). A significant association was found in Europeans under the dominant model between IL1B-511T and RA (p = 0.03, OR = 0.89, 95% CI = 0.81-0.99). Our meta-analysis indicated that IL1B ? 511-T played a protective role against RA in Europeans, and that IL1B + 3954-T had the potential to increase the risk of RA. Future large-scale studies should be considered to confirm the association between IL1B polymorphisms and RA.
文摘In this paper, we consider the problem to determine the optimal time to sell an asset that its price conforms to the Black-Schole model but its drift is a discrete random variable taking one of two given values and this probability distribution behavior changes chronologically. The result of finding the optimal strategy to sell the asset is the first time asset price falling into deterministic time-dependent boundary. Moreover, the boundary is represented by an increasing and continuous monotone function satisfying a nonlinear integral equation. We also conduct to find the empirical optimization boundary and simulate the asset price process.
文摘Under the assumption of the underlying asset is driven by the mixed fractional Brownian motion, we obtain the mixed fractionalBlack-Scholes partial differential equation by fractional Ito formula, and the pricing formula of perpetual American put option bythis partial differential equation theory.
