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 is a statistical approach used in insurance to estimate future claim liabilities by incorporating uncertainty and randomness into the reserving process. It recognizes that claim development patterns and claim frequencies can vary stochastically over time, and traditional deterministic reserving techniques may not adequately capture these uncertainties. Stochastic claims reserving methods provide a more robust and realistic estimation of future claim liabilities by considering the inherent volatility and randomness in claim data.

(i) Chain-Ladder Models:
The chain-ladder method is a commonly used deterministic reserving technique that estimates future claim liabilities based on historical claim development patterns. However, it assumes that these historical patterns will continue to hold in the future, disregarding the inherent uncertainty in claim data.

Stochastic chain-ladder models enhance the traditional chain-ladder method by introducing stochastic elements into the reserving process. These models incorporate statistical distributions to capture the variability in claim development patterns and provide a range of possible outcomes for future claim liabilities.

To implement a stochastic chain-ladder model, the following steps are typically followed:

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