Efficient valuation of variable annuities under regime-switching jump diffusion models with surrender risk and mortality risk

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-07-30 DOI:10.1016/j.cnsns.2024.108246

Wei Zhong , Zhimin Zhang , Zhenyu Cui

引用次数: 0

Abstract

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.

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具有退保风险和死亡率风险的制度转换跃迁扩散模型下变额年金的有效估值

我们提出了一种在制度转换跃迁扩散模型中对嵌入变额年金合同中的保证最低积累给付、保证最低死亡给付和退保给付进行有效估值的方法。我们在合同中加入了死亡率和退保风险，这些事件通常在保单有效期内进行离散监控。通过结合使用连续时间马尔可夫链（CTMC）近似和傅立叶余弦级数展开（COS）方法，我们确定估值问题可以在制度切换跃迁扩散框架内得到解决。大量的数值实验证明了所提方法的效率，与蒙特卡罗（MC）模拟等现有方法相比，该方法更具优势。深入的分析探讨了模型参数如何影响估值结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.