scholarly journals INTEGRAL EQUATIONS AND ACTUARIAL RISK MANAGEMENT: SOME MODELS AND NUMERICS

2003 ◽  
Vol 8 (2) ◽  
pp. 143-154 ◽  
Author(s):  
A. Makroglou
Keyword(s):  
Risk Management ◽  
Differential Equations ◽  
Integral Equations ◽  
Computational Methods ◽  
Finite Time ◽  
Numerical Results ◽  
Insurance Company ◽  
Type Approximation ◽  
Actuarial Risk ◽  
Ruin Problem

The problem of the estimation of the probability R(z, t) (here t is time, z is initial reserve) of the finite time non‐ruin problem for a risk business such as an insurance company is considered, with respect to presenting models that have been used in the literature in the form of integral / integro-differential equations, reviewing some analytical and computational methods used for their solution, presenting numerical results obtained with one method (a global Lagrange type approximation in the z—space).

scholarly journals New Solutions for System of Fractional Integro-Differential Equations and Abel’s Integral Equations by Chebyshev Spectral Method

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Hassan A. Zedan ◽  
Seham Sh. Tantawy ◽  
Yara M. Sayed
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Integral Equations ◽  
Spectral Method ◽  
Operational Matrix ◽  
Numerical Results ◽  
Efficient Technique ◽  
Test Problems ◽  
Chebyshev Spectral Method

Chebyshev spectral method based on operational matrix is applied to both systems of fractional integro-differential equations and Abel’s integral equations. Some test problems, for which the exact solution is known, are considered. Numerical results with comparisons are made to confirm the reliability of the method. Chebyshev spectral method may be considered as alternative and efficient technique for finding the approximation of system of fractional integro-differential equations and Abel’s integral equations.

Some Feller and Osgood type criteria for semilinear stochastic differential equations

2017 ◽  
Vol 17 (02) ◽  
pp. 1750011
Author(s):  
Jorge A. León ◽  
Liliana Peralta
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Integral Equations ◽  
Comparison Theorem ◽  
Finite Time ◽  
Blow Up ◽  
Continuous Process ◽  
Random Variable ◽  
Measurable Random Variable

By means of Itô’s formula and a comparison theorem for integral equations, we study the blow up in finite time of semilinear stochastic differential equations of the form [Formula: see text] Here, [Formula: see text] is non-negative and non-decreasing by components, [Formula: see text] is a predictable and continuous process, [Formula: see text] is an [Formula: see text]-Brownian motion and [Formula: see text] is an [Formula: see text]-measurable random variable. The results of this paper can be seen as extensions of the Feller and Osgood criteria.

scholarly journals Risk Management in nursing homes: an Italian experience in 2019

2020 ◽  
Vol 30 (Supplement_5) ◽  
Author(s):  
M F Furmenti ◽  
F Bert ◽  
M Rucci ◽  
U Fiandra ◽  
A Scarmozzino ◽  
...  
Keyword(s):  
Risk Management ◽  
Nursing Homes ◽  
Management Practices ◽  
Well Being ◽  
The Elderly ◽  
Management Plan ◽  
Management Policy ◽  
Insurance Company ◽  
Term Care ◽  
Starting Point

Abstract Background The ageing of the European population leads to an increasing demand for Long-Term Care services. The security and well-being of the elderly population hosted in nursing homes (NHs) needs an effective Risk Management policy, officially sanctioned in Italy by the so-called “Legge Gelli” n.24 (March 8th, 2017) and the Directive 2011/24/EU on the application of patients' rights in cross-border healthcare. In order to verify the effective application of common “best practices” in terms of Risk Management in NHs, a tool useful to analyse risk management attitudes in Northern Italy was conceived and applied in a sample of NHs. Methods The tool, developed in collaboration with the health insurance company SHAM Italia, is composed of 124 items (with a dichotomous answer -YES/NO) on topics related to various Risk Management practices. This tool was submitted in a face-to-face interview to several Directors (Health Directors or Nursing Coordinators) of NHs in the Piedmont Region. A list of randomly-chosen NHs was contacted: 4 of them were selected for the pilot study and compiled the questionnaire. Answers were gathered and analyzed through Microsoft Excel. Results Only the 25% of NHs has a Risk Management plan with objectives and indicators of effectiveness and uses Risk Analysis instruments for a pre- and post-” risk detection. Only one has employees working mainly on Risk Management alone. The 75% of the reported events were “Adverse Events”, and all the NHs (100%) have a protocol for a patient voluntary departure or for fall prevention or for bedsores prevention; while 50% have a protocol for prevention of aggressions towards operators or for patients' suicide prevention. Conclusions This work provides a starting point to face new challenges that are looming on the European Health-care Systems: the care for the elderlies needs to be perfected to reduce inefficiencies, cut useless costs and improve safety of patients in the NHs setting. Key messages Despite safety of older patients in nursing homes is not only important but mandatory in Italy, risk management tools for this setting are lacking in literature. A new tool applied in Italian nursing homes showed that risk management needs to be implemented in practice and these results can be extended to European context.

Using the generalized Adams-Bashforth-Moulton method for obtaining the numerical solution of some variable-order fractional dynamical models

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohamed M. Khader
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Numerical Solution ◽  
Numerical Results ◽  
Convergence Order ◽  
Variable Order ◽  
Numerical Treatment ◽  
Dynamical Models ◽  
Fractional Modeling ◽  
Dynamics Problems

AbstractThis paper is devoted to introduce a numerical treatment using the generalized Adams-Bashforth-Moulton method for some of the variable-order fractional modeling dynamics problems, such as Riccati and Logistic differential equations. The fractional derivative is described in Caputo variable-order fractional sense. The obtained numerical results of the proposed models show the simplicity and efficiency of the proposed method. Moreover, the convergence order of the method is also estimated numerically.

A finite-time ruin probability formula for continuous claim severities

2004 ◽  
Vol 41 (2) ◽  
pp. 570-578 ◽  
Author(s):  
Zvetan G. Ignatov ◽  
Vladimir K. Kaishev
Keyword(s):  
Real Function ◽  
Finite Time ◽  
Ruin Probability ◽  
Joint Distribution ◽  
Time Interval ◽  
Insurance Company ◽  
Finite Time Interval ◽  
Appell Polynomials ◽  
Premium Income ◽  
Inverted Dirichlet

An explicit formula for the probability of nonruin of an insurance company in a finite time interval is derived, assuming Poisson claim arrivals, any continuous joint distribution of the claim amounts and any nonnegative, increasing real function representing its premium income. The formula is compact and expresses the nonruin probability in terms of Appell polynomials. An example, illustrating its numerical convenience, is also given in the case of inverted Dirichlet-distributed claims and a linearly increasing premium-income function.

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