Taylor-series Expansion for Multivariate Characteristics of Classical Risk Processes
نویسنده
چکیده
For the continuous-time risk model with compound Poisson input, the ((nite-horizont) joint probability P (t; X x; Y y) of ruin time , surplus X just before ruin and deecit Y at ruin time is considered as a function of the arrival rate of claims. It is expanded into a Taylor series at = 0. A certain extension of a corresponding result for innnite-horizont joint probabilities, which previously has been derived in Gerber, Goovaerts and Kaas (1987), is also given. For each n 1 , the coeecient of n is determined by using a general representation formula for the derivatives of a wide class of functionals of independently marked Poisson processes.
منابع مشابه
NUMERICAL APPROACH TO SOLVE SINGULAR INTEGRAL EQUATIONS USING BPFS AND TAYLOR SERIES EXPANSION
In this paper, we give a numerical approach for approximating the solution of second kind Volterra integral equation with Logarithmic kernel using Block Pulse Functions (BPFs) and Taylor series expansion. Also, error analysis shows efficiency and applicability of the presented method. Finally, some numerical examples with exact solution are given.
متن کاملThe Development and Application of the RCW Method for the Solution of the Blasius Problem
In this research, a numerical algorithm is employed to investigate the classical Blasius equation which is the governing equation of boundary layer problem. The base of this algorithm is on the development of RCW (Rahmanzadeh-Cai-White) method. In fact, in the current work, an attempt is made to solve the Blasius equation by using the sum of Taylor and Fourier series. While, in the most common ...
متن کاملA HOMOTOPY PERTURBATION ALGORITHM AND TAYLOR SERIES EXPANSION METHOD TO SOLVE A SYSTEM OF SECOND KIND FREDHOLM INTEGRAL EQUATIONS
In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.
متن کاملExternal and Internal Incompressible Viscous Flows Computation using Taylor Series Expansion and Least Square based Lattice Boltzmann Method
The lattice Boltzmann method (LBM) has recently become an alternative and promising computational fluid dynamics approach for simulating complex fluid flows. Despite its enormous success in many practical applications, the standard LBM is restricted to the lattice uniformity in the physical space. This is the main drawback of the standard LBM for flow problems with complex geometry. Several app...
متن کاملModeling of Nonlinear Systems with Friction Structure Using Multivariable Taylor Series Expansion
The major aim of this article is modeling of nonlinear systems with friction structure that, thismethod is essentially extended based on taylore expansion polynomial. So in this study, thetaylore expansion was extended in the generalized form for the differential equations of the statespaceform. The proposed structure is based on multi independent variables taylore extended.According to the pro...
متن کامل