TITLE

NECESSARY AND SUFFICIENT CONDITION FOR THE BOUNDEDNESS OF THE GERBER-SHIU FUNCTION IN DEPENDENT SPARRE ANDERSEN MODEL

AUTHOR(S)
ORBÁN-MIHÁLYKÓ, ÉVA; MIHÁLYKÓ, CSABA
PUB. DATE
January 2014
SOURCE
Miskolc Mathematical Notes;2014, Vol. 15 Issue 1, p159
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper we investigate the boundedness of the Gerber-Shiu expected discounted penalty function applied in insurance mathematics. We give a necessary and sufficient condition for its boundedness. This condition is essentially the boundedness of the conditional expectation given the ruin occurs at the first claim. It assures that the integral equation satisfied by the Gerber- Shiu function has a unique bounded solution and it is exactly the Gerber-Shiu function. By the help of the proven necessary and sufficient condition we can also simplify the theorem concerning the necessary and sufficient condition for the limit property. We do not assume independence between the inter-claim time and the claim size but the results can be applied to the usually investigated independent case as well. We present examples to show the applicability of the condition.
ACCESSION #
97250475

 

Related Articles

  • On a representation of the solution of the inverse Sturm-Liouville problem on the entire line. Zhura, N.; Soldatov, A. // Differential Equations;Aug2015, Vol. 51 Issue 8, p1022 

    We obtain sufficient conditions for the fundamental Faddeev-Marchenko theorem to be true. In addition, we derive a representation of the solution of the inverse Sturm-Liouville problem on the entire line on the basis of the solution of a boundary value problem for the Jost functions and the...

  • Boundary value problem for an advanced-retarded equation of mixed type with a nonsmooth degeneration line. Zarubin, A. // Differential Equations;Oct2014, Vol. 50 Issue 10, p1352 

    We consider the Tricomi problem for an equation of mixed type with the Lavrent'ev-Bitsadze operator in the leading part, with advanced-retarded arguments, and with parallel degeneration lines. We prove the uniqueness theorem under restrictions on the values of the argument deviations. The...

  • NONNEGATIVE SOLUTIONS TO AN INTEGRAL EQUATION AND ITS APPLICATIONS TO SYSTEMS OF BOUNDARY VALUE PROBLEMS. PURNARAS, IOANNIS K. // Electronic Journal of Differential Equations;2009, Vol. 2009, Special section p1 

    We study the existence of positive eigenvalues yielding nonnegative solutions to an integral equation. Also we study the positivity of solutions on specific sets. These results are obtained by using a fixed point theorem in cones and are illustrated by application to systems of boundary value...

  • On the nonuniqueness of the solution of the Tricomi problem with the generalized Frankl matching condition. Moiseev, T. // Differential Equations;Oct2014, Vol. 50 Issue 10, p1378 

    We obtain an integral representation of the solution of the Tricomi problem for the Lavrent'ev-Bitsadze equation with mixed boundary conditions in the elliptic part of the domain and with zero posed on one characteristic of the equation. The gradient of the solution is not continuous but...

  • THE DUAL INTEGRAL EQUATION METHOD IN HYDROMECHANICAL SYSTEMS. KAVALLARIS, N. I.; ZISIS, V. // Journal of Applied Mathematics;2009, Special section p447 

    Some hydromechanical systems are investigated by applying the dual integral equation method. In developing this method we suggest from elementary appropriate solutions of Laplace's equation, in the domain under consideration, the introduction of a potential function which provides useful...

  • Adjoint and self-adjoint boundary value problems on a geometric graph. Zavgorodnij, M. // Differential Equations;Apr2014, Vol. 50 Issue 4, p441 

    We consider boundary value problems of arbitrary order for linear differential equations on a geometric graph. Solutions of boundary value problems are coordinated at the interior vertices of the graph and satisfy given conditions at the boundary vertices. For considered boundary value problems,...

  • MULTIPLE SOLUTIONS FOR DIRICHLET NONLINEAR BVPS INVOLVING FRACTIONAL LAPLACIAN. KULCZYCKI, TADEUSZ; STAŃCZY, ROBERT // Discrete & Continuous Dynamical Systems - Series B;Oct2014, Vol. 19 Issue 8, p2581 

    The existence of at least two solutions to superlinear integral equation in cone is proved using the Krasnosielskii Fixed Point Theorem. The result is applied to the Dirichlet BVPs with the fractional Laplacian.

  • PERIODIC SOLUTIONS TO DIFFERENTIAL EQUATIONS WITH A GENERALIZED P-LAPLACIAN. LIPOWSKI, ADAM; PRZERADZKI, BOGDAN; SZYMAŃSKA-DĘBOWSKA, KATARZYNA // Discrete & Continuous Dynamical Systems - Series B;Oct2014, Vol. 19 Issue 8, p2593 

    The existence of a periodic solution to nonlinear ODEs with φ-Laplacian is proved under conditions on functions given in the equation (not on the unknown solutions). The results are applied to a relativistic pendulum equation in a general form.

  • Solvability of Third-Order Three-Point Boundary Value Problems. Dongyuan Liu; Zigen Ouyang // Abstract & Applied Analysis;2014, p1 

    We are interested in the existence theorems for a third-order three-point boundary value problem. In the nonresonant case, using the Krasnosel'skii fixed point theorem, we obtain some sufficient conditions for the existence of the positive solutions. In addition, we focus on the resonant case,...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics