Dissertation > Excellent graduate degree dissertation topics show

On the Risk Model Involving Two Classes of Claims with Threshold Dividend Strategy

Author: LiShiJun
Tutor: MingRuiXing
School: Jiangxi Normal University
Course: Probability Theory and Mathematical Statistics
Keywords: double compound Poisson process Erlang(n) risk process thresh-old dividend strategy the value function the expected discounted penalty func-tion Integro-differential equations
CLC: O211.67
Type: Master's thesis
Year: 2011
Downloads: 4
Quote: 0
Read: Download Dissertation

Abstract


In this thesis, we consider a risk model with two independent classes of insurancerisks. The expected discounted penalty (Gerber-Shiu ) function and the expectationof the present value of all dividends until ruin (the value function) for the risk modelon a threshold dividend strategy are studied. The thesis is divided into 5 chapters.In chapter 1, the classical compound Poisson risk model, the risk model in-volving two independent classes of insurance risks and two core problems in theactuarial literature, the expected discounted penalty function and dividend strategyare introduced. Some corresponding developments in recent years are also reviewed.In chapter 2, we consider a double compound Poisson risk model involving twoindependent Poisson processes. A system of integro-differential equations of theexpected discounted penalty function is derived. We also analyze the expected dis-counted penalty function. When 0≤u < b, the Laplace transform method is appliedand consequently the explicit expression for the expected discounted penalty func-tion is derived when the claims from the two classes are exponentially distributed.When u≥b, a system of the renewal equations for the expected discounted penaltyfunction is obtained.In chapter 3, we study the value function in the double compound Poissonrisk model with the threshold dividend strategy. Integro-differential equations withcertain boundary conditions for the present value of dividends until ruin are de-rived. When the claim size distributions are exponentially distributed, we obtainthe explicit expressions for the value function and show that the threshold dividendstrategy is an optimal dividend strategy.In chapter 4, a risk model involving Poisson and Erlang(n) risk processes isstudied. We derive a system of integro-differential equations of the expected dis-counted penalty function. The Laplace transform method and the renewal equationmethod are applied to analyze the expected discounted penalty function.In chapter 5, we study the value function in the risk model involving Poisson andErlang(n) processes. Integro-differential equations with certain boundary conditionsfor the present value of dividends until ruin are derived, the explicit expression ofthe value function and the problem of the optimal dividend strategy should bereserved for further consideration, since it is diffcult to solve the corresponding integro-differential equations.

Related Dissertations

  1. Study on the Sportswear Brand Community Based on Network Platform,F273.2;F224
  2. Research on Reinforcement Learning Based on Value Function Approximation and State Space Decomposition,TP242
  3. Research on Mobile Phone Chain Retail Enterprise’s Function Change and Their Marketing Strategies,F721.7
  4. The Study of Dividends and Bankruptcy in the Compound Binomial Risk Model with Dividend Strategies,F840
  5. Study of GARCH Model Based on Value Function and Risk Measurement,F831.5
  6. Numerical Stability of Linear Multistep Methods for Linear Neutral Integro-differential Equations with Many Delays,O241.8
  7. Spectral Deferred Correction Methods for Discrete and Distributed Delay Systems,O241.8
  8. Stability Analysis of a Class of Delay Integro Differential Equations,O241.8
  9. Nonconforming Finite Element Analysis for Two Classes of Evolution Differential Equations,O241.82
  10. The Optimal Dividend Strategy in the Compound Poisson Modelwith Debit Interest,F840
  11. Existence of Boundary Value Problems for Second Order Impulsive Integro-differential Equations in Banach Spaces in Infinite Interval,O175.6
  12. The Penalty Function、 Value Function and Their Application : Dividend-Reinsurance Strategy,F840
  13. Impulsive Integro - Differential Equations existence theory and its applications,O175.5
  14. Convergenge of Waveform Relaxation Methods for Delay Integro-Differential Equations,O241.83
  15. Anti-periodic Boundary Value Problem for the Second-order Impulsive Integro-differential Equations,O175.8
  16. A Study on Skewness Risk:the Behavioral Finance Perspective,F830
  17. Semi- linear pseudo- hyperbolic Integral - differential equations H ~ 1-Galerkin Mixed Finite Element Method,O241.82
  18. From the Value to the Function,D925.1
  19. On the Value and Function of Civil Cases Mediation,D925.1
  20. A Study on Annotation to Gu Wangyan,I207.419

CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Theory of probability ( probability theory, probability theory ) > Random process > Expectations and Forecast
© 2012 www.DissertationTopic.Net  Mobile