In this paper, we study the option price theory of stochastic differential equations under G-Lévy process. By using G-It<span style="font-size:12px;white-space:nowrap;">ô</span> for...In this paper, we study the option price theory of stochastic differential equations under G-Lévy process. By using G-It<span style="font-size:12px;white-space:nowrap;">ô</span> formula and G-expectation property, we give the proof of Black-Scholes equations (Integro-PDE) under G-Lévy process. Finally, we give the simulation of G-Lévy process and the explicit solution of Black-Scholes under G-Lévy process.展开更多
With the aid of Mullin-Rota's substitution rule, we show that the Sheffertype differential operators together with the delta operators ? and D could be used to construct a pair of expansion formulas that imply a w...With the aid of Mullin-Rota's substitution rule, we show that the Sheffertype differential operators together with the delta operators ? and D could be used to construct a pair of expansion formulas that imply a wide variety of summation formulas in the discrete analysis and combinatorics. A convergence theorem is established for a fruitful source formula that implies more than 20 noted classical fomulas and identities as consequences. Numerous new formulas are also presented as illustrative examples. Finally, it is shown that a kind of lifting process can be used to produce certain chains of(∞~m) degree formulas for m ≥ 3 with m ≡ 1(mod 2) and m ≡ 1(mod 3), respectively.展开更多
This paper presents an actuarial model of life insurance for fuzzy markets based on Liu process. At first, some researches about an actuarial model of life insurance for stochastic market and concepts about fuzzy proc...This paper presents an actuarial model of life insurance for fuzzy markets based on Liu process. At first, some researches about an actuarial model of life insurance for stochastic market and concepts about fuzzy process have been reviewed. Then, an actuarial model of life insurance for fuzzy process is formulated.展开更多
Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonst...Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonstrated. We present a theorem and its proof that confirms the possibility to obtain the finite process and imposes the requirement for the matrix of SLAE. This matrix must be unipotent, i.e. all its eigenvalues to be equal to 1. An example of transformation of SLAE given analytically to the form with a unipotent matrix is presented. It is shown that splitting the unipotent matrix into identity and nilpotent ones results in Cramer’s analytical formulas in a finite number of iterations.展开更多
In this paper, according to G-Brownian motion and other related concepts and properties, we define multiple Itôintegrals driven by G-Brownian motion and G-Lévy process. By using the G-Itôformula...In this paper, according to G-Brownian motion and other related concepts and properties, we define multiple Itôintegrals driven by G-Brownian motion and G-Lévy process. By using the G-Itôformula and the properties of G-expectation, two main theorems about Itôintegral are obtained and proved. These two theorems provide powerful help for the subsequent research on jump process.展开更多
文摘In this paper, we study the option price theory of stochastic differential equations under G-Lévy process. By using G-It<span style="font-size:12px;white-space:nowrap;">ô</span> formula and G-expectation property, we give the proof of Black-Scholes equations (Integro-PDE) under G-Lévy process. Finally, we give the simulation of G-Lévy process and the explicit solution of Black-Scholes under G-Lévy process.
文摘With the aid of Mullin-Rota's substitution rule, we show that the Sheffertype differential operators together with the delta operators ? and D could be used to construct a pair of expansion formulas that imply a wide variety of summation formulas in the discrete analysis and combinatorics. A convergence theorem is established for a fruitful source formula that implies more than 20 noted classical fomulas and identities as consequences. Numerous new formulas are also presented as illustrative examples. Finally, it is shown that a kind of lifting process can be used to produce certain chains of(∞~m) degree formulas for m ≥ 3 with m ≡ 1(mod 2) and m ≡ 1(mod 3), respectively.
文摘This paper presents an actuarial model of life insurance for fuzzy markets based on Liu process. At first, some researches about an actuarial model of life insurance for stochastic market and concepts about fuzzy process have been reviewed. Then, an actuarial model of life insurance for fuzzy process is formulated.
文摘Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonstrated. We present a theorem and its proof that confirms the possibility to obtain the finite process and imposes the requirement for the matrix of SLAE. This matrix must be unipotent, i.e. all its eigenvalues to be equal to 1. An example of transformation of SLAE given analytically to the form with a unipotent matrix is presented. It is shown that splitting the unipotent matrix into identity and nilpotent ones results in Cramer’s analytical formulas in a finite number of iterations.
文摘In this paper, according to G-Brownian motion and other related concepts and properties, we define multiple Itôintegrals driven by G-Brownian motion and G-Lévy process. By using the G-Itôformula and the properties of G-expectation, two main theorems about Itôintegral are obtained and proved. These two theorems provide powerful help for the subsequent research on jump process.
