We present an efficient valuation approach for guaranteed minimum accumulation benefits (GMABs), guaranteed minimum death benefits (GMDBs), and surrender benefits (SBs) embedded in variable annuity (VA) contracts in a regime-switching jump diffusion model. We incorporate into the contract the risks of mortality and surrender, with these events generally monitored discretely over the life of the policy. Using a combination of the continuous-time Markov chain (CTMC) approximation and the Fourier cosine series expansion (COS) method, we determine that the valuation problem can be resolved within a regime-switching jump diffusion framework. Extensive numerical experiments showcase the efficiency of the proposed method, which proves to be more advantageous when compared to existing approaches like Monte Carlo (MC) simulation. The thorough analysis explores how model parameters affect the valuation outcomes.

中文翻译：

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具有退保风险和死亡风险的制度转换跳跃扩散模型下可变年金的有效估值


我们提出了一种有效的估值方法，用于在制度切换跳跃扩散模型中嵌入可变年金（VA）合同中的保证最低累积福利（GMAB）、保证最低死亡福利（GMDB）和退保福利（SB）。我们将死亡和退保风险纳入合同，通常在保单有效期内对这些事件进行离散监控。使用连续时间马尔可夫链（CTMC）近似和傅里叶余弦级数展开（COS）方法的组合，我们确定可以在状态切换跳跃扩散框架内解决估值问题。大量的数值实验展示了该方法的效率，与蒙特卡罗（MC）模拟等现有方法相比，该方法被证明更具优势。全面的分析探讨了模型参数如何影响估值结果。