Thiele's PIDE for unit-linked policies in the Heston-Hawkes stochastic volatility model

Autor:	Baños, David R., Ortiz-Latorre, Salvador, Font, Oriol Zamora
Rok vydání:	2023
Předmět:	Quantitative Finance - Pricing of Securities Mathematics - Probability 60G55 60H30 91G05 91G15
Druh dokumentu:	Working Paper
Popis:	The main purpose of the paper is to derive Thiele's differential equation for unit-linked policies in the Heston-Hawkes stochastic volatility model introduced 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 a risk neutral probability measure is possible. Studying the moments of the variance and certain stochastic exponentials, a suitable family of risk neutral probability measures is found. 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. Comment: 26 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.03541 Zobrazit plný text záznamu View this record from Arxiv