An efficient hybrid algorithm based on Monte-Carlo method for pricing catastrophic reinsurance contract under a Markov-switching stochastic turbulence model

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This paper presents a novel variance reduction strategy for pricing catastrophic reinsurance contracts in a regime-switching system using Monte-Carlo simulation. This technique combines generalized antithetic variables with importance sampling. The importance sampling problem is evaluated by formulating it as a parametric minimization problem using an equivalent measure. Since the frequent regime-switching framework leads to an imperfect market due to the presence of unhedged catastrophic risks, the pricing measure is not unique, and an appropriate measure is selected using the Esscher transform. Under this measure , the proposed estimator remains statistically unbiased. The effectiveness of the proposed method is demonstrated through numerical experiments, and the sensitivity of the contract price to key operational criteria is also assessed. The results show that the standard error decreases as the number of antithetic variables increases, and that the contract price is influenced by several factors, including catastrophe occurrence, mean loss, and values of assets and liabilities.