  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.
