Heston-Hawkes随机波动率模型中单位挂钩政策的Thiele PIDE

David R. Baños, Salvador Ortiz-Latorre, Oriol Zamora Font
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引用次数: 0

摘要

本文的主要目的是推导出在arXiv:2210.15343中提出的Heston-Hawkes随机波动模型中单位联动策略的Thiele微分方程。该模型是对著名的Heston模型的扩展,该模型通过在波动率中加入复合Hawkesprocess来结合波动率聚类特征。由于模型是无套利的,在$\mathbb{Q}$下,通过等价原则对单位挂钩政策定价是可能的。对可积性条件进行了检验,并找到了一类适合的风险中性概率测度,得到了Thiele微分方程。求解Thiele方程是目前公认的实用的寿险准备金计算方法,它对保证保险公司的偿付能力至关重要。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Thiele's PIDE for unit-linked policies in the Heston-Hawkes stochastic volatility model
The main purpose of the paper is to derive Thiele's differential equation for unit-linked policies in the Heston-Hawkes stochastic volatility model presented in arXiv:2210.15343. This model is an extension of the well-known Heston model that incorporates the volatility clustering feature by adding a compound Hawkes process in the volatility. Since the model is arbitrage-free, pricing unit-linked policies via the equivalence principle under $\mathbb{Q}$ is possible. Some integrability conditions are checked and a suitable family of risk neutral probability measures is found to obtain Thiele's differential equation. The established and practical method to compute reserves in life insurance is by solving Thiele's equation, which is crucial to guarantee the solvency of the insurance company.
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