Two kinds of mathematical expressions of stock price, one of which based on certain description is the solution of the simplest differential equation (S.D.E.) obtained by method similar to that used in solid mechanics...Two kinds of mathematical expressions of stock price, one of which based on certain description is the solution of the simplest differential equation (S.D.E.) obtained by method similar to that used in solid mechanics,the other based on uncertain description (i.e., the statistic theory)is the assumption of Black_Scholes's model (A.B_S.M.) in which the density function of stock price obeys logarithmic normal distribution, can be shown to be completely the same under certain equivalence relation of coefficients. The range of the solution of S.D.E. has been shown to be suited only for normal cases (no profit, or lost profit news, etc.) of stock market, so the same range is suited for A.B_ S.M. as well.展开更多
The development of Backward Stochastic Differential Equation Theory is just a thing happened in the past years. Although its development and application is far behind Forward Stochastic Differential Equation, its wide...The development of Backward Stochastic Differential Equation Theory is just a thing happened in the past years. Although its development and application is far behind Forward Stochastic Differential Equation, its wide application prospect on financial mathematics gets more and more attention. The meaning of Backward Stochastic Differential Equation is that change a already-known final （usually uncertain） goal into a present certain answer to make a present resolution. But Insurance Pricing happens to know the final result, it＇ s certain that the result is uncertain, that is to say, to get out of danger or not. And then make present insurance price according to the future uncertain result. The Insurance Pricing just follows the meaning of Backward Stochastic Differential Equation. Insurance Pricing itself is also a research field sprang up in past scores of years, because insurance pricing is the indisputable core of insurance work, and gets quite a few researchers＇ attention. This article adopts backward stochastic differential equation theory and do research on problem about technology insurance pricing.展开更多
The primary objective of this research article is to introduce Differential Evolution (DE) algorithm for solving bidding strategy in deregulated power market. Suppliers (GENCOs) and consumers (DISCOs) participate in t...The primary objective of this research article is to introduce Differential Evolution (DE) algorithm for solving bidding strategy in deregulated power market. Suppliers (GENCOs) and consumers (DISCOs) participate in the bidding process in order to maximize the profit of suppliers and benefits of the consumers. Each supplier bids strategically by choosing the bidding coefficients to counter the competitors bidding strategy. Electricity or electric power is traded through bidding in the power exchange. GENCOs sell energy to power exchange and in turn ancillary services to Independent System Operator (ISO). In this paper, Differential Evolution algorithm is proposed for solving bidding strategy problem in operation of power system under deregulated environment. An IEEE 30 bus system with six generators and two large consumers is employed to demonstrate the proposed technique. The results show the adaptability of the proposed method compared with Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Monte Carlo simulation in terms of Market Clearing Price (MCP).展开更多
In this article we derive a general differential equation that describes long-term economic growth in terms of cyclical and trend components. Equation is based on the model of non-linear accelerator of induced investm...In this article we derive a general differential equation that describes long-term economic growth in terms of cyclical and trend components. Equation is based on the model of non-linear accelerator of induced investment. A scheme is proposed for obtaining approximate solutions of nonlinear differential equation by splitting solution into the rapidly oscillating business cycles and slowly varying trend using Krylov-Bogoliubov-Mitropolsky averaging. Simplest modes of the economic system are described. Characteristics of the bifurcation point are found and bifurcation phenomenon is interpreted as loss of stability making the economic system available to structural change and accepting innovations. System being in a nonequilibrium state has a dynamics with self-sustained undamped oscillations. The model is verified with economic development of the US during the fifth Kondratieff cycle (1982-2010). Model adequately describes real process of economic growth in both quantitative and qualitative aspects. It is one of major results that the model gives a rough estimation of critical points of system stability loss and falling into a crisis recession. The model is used to forecast the macroeconomic dynamics of the US during the sixth Kondratieff cycle (2018-2050). For this forecast we use fixed production capital functional dependence on a long-term Kondratieff cycle and medium-term Juglar and Kuznets cycles. More accurate estimations of the time of crisis and recession are based on the model of accelerating log-periodic oscillations. The explosive growth of the prices of highly liquid commodities such as gold and oil is taken as real predictors of the global financial crisis. The second wave of crisis is expected to come in June 2011.展开更多
在不确定市场需求和回收数量的背景下,将决策者风险规避行为纳入到闭环供应链中,研究决策者风险规避系数、消费者WTP(willing to pay)、不确定性水平对闭环供应链的定价影响。研究发现:决策者的风险规避系数会间接影响回收价格;消费者WT...在不确定市场需求和回收数量的背景下,将决策者风险规避行为纳入到闭环供应链中,研究决策者风险规避系数、消费者WTP(willing to pay)、不确定性水平对闭环供应链的定价影响。研究发现:决策者的风险规避系数会间接影响回收价格;消费者WTP对再制品销售价格总是有利的,但对新产品销售价格和回收价格的影响与决策者风向规避特性有关;不确定性水平对定价决策的影响与风险持有者有关。展开更多
This paper presents two new versions of uncertain market models for valuing vulnerable European call option.The dynamics of underlying asset,counterparty asset,and corporate liability are formulated on the basis of un...This paper presents two new versions of uncertain market models for valuing vulnerable European call option.The dynamics of underlying asset,counterparty asset,and corporate liability are formulated on the basis of uncertain differential equations and uncertain fractional differential equations of Caputo type,respectively,and the solution to an uncertain fractional differential equation of Caputo type is presented by employing the Mittag-Leffler function andα-path.Then,the pricing formulas of vulnerable European call option based on the proposed models are investigated as well as some algorithms.Some numerical experiments are performed to verify the effectiveness of the results.展开更多
文摘Two kinds of mathematical expressions of stock price, one of which based on certain description is the solution of the simplest differential equation (S.D.E.) obtained by method similar to that used in solid mechanics,the other based on uncertain description (i.e., the statistic theory)is the assumption of Black_Scholes's model (A.B_S.M.) in which the density function of stock price obeys logarithmic normal distribution, can be shown to be completely the same under certain equivalence relation of coefficients. The range of the solution of S.D.E. has been shown to be suited only for normal cases (no profit, or lost profit news, etc.) of stock market, so the same range is suited for A.B_ S.M. as well.
文摘The development of Backward Stochastic Differential Equation Theory is just a thing happened in the past years. Although its development and application is far behind Forward Stochastic Differential Equation, its wide application prospect on financial mathematics gets more and more attention. The meaning of Backward Stochastic Differential Equation is that change a already-known final （usually uncertain） goal into a present certain answer to make a present resolution. But Insurance Pricing happens to know the final result, it＇ s certain that the result is uncertain, that is to say, to get out of danger or not. And then make present insurance price according to the future uncertain result. The Insurance Pricing just follows the meaning of Backward Stochastic Differential Equation. Insurance Pricing itself is also a research field sprang up in past scores of years, because insurance pricing is the indisputable core of insurance work, and gets quite a few researchers＇ attention. This article adopts backward stochastic differential equation theory and do research on problem about technology insurance pricing.
文摘The primary objective of this research article is to introduce Differential Evolution (DE) algorithm for solving bidding strategy in deregulated power market. Suppliers (GENCOs) and consumers (DISCOs) participate in the bidding process in order to maximize the profit of suppliers and benefits of the consumers. Each supplier bids strategically by choosing the bidding coefficients to counter the competitors bidding strategy. Electricity or electric power is traded through bidding in the power exchange. GENCOs sell energy to power exchange and in turn ancillary services to Independent System Operator (ISO). In this paper, Differential Evolution algorithm is proposed for solving bidding strategy problem in operation of power system under deregulated environment. An IEEE 30 bus system with six generators and two large consumers is employed to demonstrate the proposed technique. The results show the adaptability of the proposed method compared with Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Monte Carlo simulation in terms of Market Clearing Price (MCP).
文摘In this article we derive a general differential equation that describes long-term economic growth in terms of cyclical and trend components. Equation is based on the model of non-linear accelerator of induced investment. A scheme is proposed for obtaining approximate solutions of nonlinear differential equation by splitting solution into the rapidly oscillating business cycles and slowly varying trend using Krylov-Bogoliubov-Mitropolsky averaging. Simplest modes of the economic system are described. Characteristics of the bifurcation point are found and bifurcation phenomenon is interpreted as loss of stability making the economic system available to structural change and accepting innovations. System being in a nonequilibrium state has a dynamics with self-sustained undamped oscillations. The model is verified with economic development of the US during the fifth Kondratieff cycle (1982-2010). Model adequately describes real process of economic growth in both quantitative and qualitative aspects. It is one of major results that the model gives a rough estimation of critical points of system stability loss and falling into a crisis recession. The model is used to forecast the macroeconomic dynamics of the US during the sixth Kondratieff cycle (2018-2050). For this forecast we use fixed production capital functional dependence on a long-term Kondratieff cycle and medium-term Juglar and Kuznets cycles. More accurate estimations of the time of crisis and recession are based on the model of accelerating log-periodic oscillations. The explosive growth of the prices of highly liquid commodities such as gold and oil is taken as real predictors of the global financial crisis. The second wave of crisis is expected to come in June 2011.
文摘在不确定市场需求和回收数量的背景下,将决策者风险规避行为纳入到闭环供应链中,研究决策者风险规避系数、消费者WTP(willing to pay)、不确定性水平对闭环供应链的定价影响。研究发现:决策者的风险规避系数会间接影响回收价格;消费者WTP对再制品销售价格总是有利的,但对新产品销售价格和回收价格的影响与决策者风向规避特性有关;不确定性水平对定价决策的影响与风险持有者有关。
基金supported by the National Natural Science Foundation of China under Grant Nos.11871010 and 11971040by the Fundamental Research Funds for the Central Universities under Grant No.2019XD-A11supported by the National Natural Science Foundation of China under Grant No.71073020.
文摘This paper presents two new versions of uncertain market models for valuing vulnerable European call option.The dynamics of underlying asset,counterparty asset,and corporate liability are formulated on the basis of uncertain differential equations and uncertain fractional differential equations of Caputo type,respectively,and the solution to an uncertain fractional differential equation of Caputo type is presented by employing the Mittag-Leffler function andα-path.Then,the pricing formulas of vulnerable European call option based on the proposed models are investigated as well as some algorithms.Some numerical experiments are performed to verify the effectiveness of the results.
