What is meant by Stochastic Claims Reserving? Discuss this in the contexts of (i) Chain-Ladder Models and (ii) Over-Dispersed Poisson Model

Stochastic Claims Reserving:
Stochastic claims reserving involves incorporating randomness into the estimation of future insurance claims reserves.

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It recognizes that the actual development of insurance claims can be influenced by uncertain factors, and stochastic models account for this variability.

(i) Chain-Ladder Models:

• In a stochastic context, Chain-Ladder Models are extended to include random variability in the claims development process.
• Monte Carlo simulations are often used to generate multiple possible future claim development patterns.
• By considering a range of potential outcomes, stochastic Chain-Ladder Models provide a more comprehensive view of the uncertainty associated with claims reserves.

(ii) Over-Dispersed Poisson Model:

• Over-Dispersed Poisson Models are used to address situations where the assumption of Poisson distribution (constant claim frequency) is too restrictive.
• Stochasticity in this context involves introducing variability in claim frequency beyond what is expected in a Poisson distribution.
• The model accounts for over-dispersion by allowing for more variability, reflecting the randomness and unpredictability in the occurrence of claims.

In summary, stochastic claims reserving introduces randomness into the estimation process, and both Chain-Ladder Models and Over-Dispersed Poisson Models are adapted to incorporate this stochastic nature, providing a more realistic and probabilistic approach to estimating claims reserves.