Risk-Free Investments and Their Comparison with Simple Risky Strategies in Pension Insurance Model: Solving Singular Problems for Integro-Differential Equations

2020 ◽  
Vol 60 (10) ◽  
pp. 1621-1641
Author(s):  
T. A. Belkina ◽  
N. B. Konyukhova ◽  
B. V. Slavko
Keyword(s):  
Differential Equations ◽  
Pension Insurance ◽  
Singular Problems ◽  
Insurance Model

Nonlinear Differential Equations and Feedback Control Design for the Urban–Rural Resident Pension Insurance in China

2015 ◽  
Vol 25 (14) ◽  
pp. 1540029
Author(s):  
Lijian Wang
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Control Design ◽  
Rural Resident ◽  
Pension Insurance ◽  
Modern Control Theory ◽  
Insurance System ◽  
Urban Rural ◽  
Pension Insurance System

Facing many problems of the urban–rural resident pension insurance system in China, one should firstly make sure that this system can be optimized. This paper, based on the modern control theory, sets up differential equations as models to describe the urban–rural resident pension insurance system, and discusses the globally asymptotic stability in the sense of Liapunov for the urban–rural resident pension insurance system in the new equilibrium point. This research sets the stage for our further discussion, and it is theoretically important and convenient for optimizing the urban–rural resident pension insurance system.

ROBUST FILTERING AND DETECTION OF AN INSURANCE MODEL

2007 ◽  
Vol 07 (01) ◽  
pp. 91-102 ◽  
Author(s):  
LAKHDAR AGGOUN
Keyword(s):  
Differential Equations ◽  
Stochastic Models ◽  
Point Processes ◽  
Risk Theory ◽  
Robust Filtering ◽  
Stochastic Integration ◽  
Competing Models ◽  
Rate Processes ◽  
The Difference ◽  
Insurance Model

Risk theory deals with stochastic models in insurance business. Usually, in such models claims are described by point processes and the amounts claimed by policy holders are sequences of random variables. The profit or loss, of the company is the difference between premiums income and the claims. We assume that we have a certain number of competing models, describing the claims and premiums rate processes. We are interested in ranking the candidate models based on their likelihood of being most appropriate for describing these processes. We compute robust dynamics for our estimates. In these new dynamics stochastic integration disappear and stochastic differential equations become ordinary differential equations.

scholarly journals IMPULSIVE PERIODIC SOLUTIONS FOR SINGULAR PROBLEMS VIA VARIATIONAL METHODS

2012 ◽  
Vol 86 (2) ◽  
pp. 193-204 ◽  
Author(s):  
JUNTAO SUN ◽  
DONAL O’REGAN
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Periodic Solutions ◽  
Mountain Pass Theorem ◽  
Second Order ◽  
Mountain Pass ◽  
Singular Problems ◽  
Singular Differential Equations

AbstractIn this paper we study impulsive periodic solutions for second-order nonautonomous singular differential equations. Our proof is based on the mountain pass theorem. Some recent results in the literature are extended.

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