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International Journal of Engineering, Mathematical and Physical Sciences

ISSN: 2517-9934

Total 23 content found

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The Dividend Payments for General Claim Size Distributions under Interest Rate

Year: 2007 Volume: 1 Issue: 1 10 - 13 Pages

Abstract: This paper evaluates the dividend payments for general claim size distributions in the presence of a dividend barrier. The surplus of a company is modeled using the classical risk process perturbed by diffusion, and in addition, it is assumed to accrue interest at a constant rate. After presenting the integro-differential equation with initial conditions that dividend payments satisfies, the paper derives a useful expression of the dividend payments by employing the theory of Volterra equation. Furthermore, the optimal value of dividend barrier is found. Finally, numerical examples illustrate the optimality of optimal dividend barrier and the effects of parameters on dividend payments.

The Number of Rational Points on Conics Cp,k : x2 − ky2 = 1 over Finite Fields Fp

Year: 2007 Volume: 1 Issue: 1 6 - 9 Pages

Abstract: Let p be a prime number, Fp be a finite field, and let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively.