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Related Concept Videos

Hazard Rate01:11

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The hazard rate, also known as the hazard function or failure rate, is a statistical measure used to describe the instantaneous rate at which an event occurs, given that the event has not yet happened. From a probabilistic perspective, it represents the likelihood that a subject will experience the event in a very small time interval, conditional on surviving up to the beginning of that interval. In terms of frequency, the hazard rate can be viewed as the ratio of the number of events to the...
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Introduction To Survival Analysis01:18

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Survival analysis is a statistical method used to study time-to-event data, where the "event" might represent outcomes like death, disease relapse, system failure, or recovery. A unique feature of survival data is censoring, which occurs when the event of interest has not been observed for some individuals during the study period. This requires specialized techniques to handle incomplete data effectively.
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Assumptions of Survival Analysis01:15

Assumptions of Survival Analysis

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Survival models analyze the time until one or more events occur, such as death in biological organisms or failure in mechanical systems. These models are widely used across fields like medicine, biology, engineering, and public health to study time-to-event phenomena. To ensure accurate results, survival analysis relies on key assumptions and careful study design.
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Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
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Survival Tree01:19

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Survival trees are a non-parametric method used in survival analysis to model the relationship between a set of covariates and the time until an event of interest occurs, often referred to as the "time-to-event" or "survival time." This method is particularly useful when dealing with censored data, where the event has not occurred for some individuals by the end of the study period, or when the exact time of the event is unknown.
 Building a Survival Tree
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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Related Experiment Video

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An R-Based Landscape Validation of a Competing Risk Model
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Ruin Analysis on a New Risk Model with Stochastic Premiums and Dependence Based on Time Series for Count Random

Lihong Guan1, Xiaohong Wang2

  • 1School of Science, Changchun University, Changchun 130022, China.

Entropy (Basel, Switzerland)
|May 16, 2023
PubMed
Summary

This study introduces a discrete-time insurance risk model using integer-valued autoregressive and moving average processes for premiums and claims. It provides formulas for ruin probability, crucial for actuarial risk management.

Keywords:
INAR(1) processINMA(1) processrisk modelruin probabilitystochastic premiums

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Area of Science:

  • Actuarial Science
  • Quantitative Finance
  • Probability Theory

Background:

  • Insurance risk models are essential for financial stability.
  • Understanding temporal dependence in claims and premiums is critical.
  • Existing models may not fully capture complex dependencies.

Purpose of the Study:

  • To develop a novel discrete-time risk model for insurance portfolios.
  • To incorporate stochastic premiums and specific temporal dependence structures.
  • To quantitatively assess insurance portfolio risk and ruin probabilities.

Main Methods:

  • Utilizing a first-order integer-valued autoregressive (INAR(1)) process for premium numbers.
  • Employing an integer-valued moving average (INMA(1)) process for claim numbers.
  • Deriving explicit expressions for the Lundberg adjustment coefficient and ruin probability formulas.

Main Results:

  • Established the Lundberg approximation formula for infinite-time ruin probability.
  • Derived asymptotic formulas for finite-time ruin probability with heavy-tailed claim sizes.
  • Demonstrated model applicability through two numerical examples.

Conclusions:

  • The proposed model effectively captures temporal dependencies in insurance portfolios.
  • The derived formulas provide robust tools for quantitative risk assessment.
  • Findings contribute to a deeper understanding of ruin theory in actuarial science.