arXiv subjects

Philipp C. Hornung

Publications and source records attributed to Philipp C. Hornung.

3 recordsLinked to original sources

arXiv2026

Robust Control for Marked Point Processes under Transition-Rate Uncertainty

We consider a novel robust utility maximisation problem under bounded cumulative transition rate uncertainty within the class of non-Markovian marked point processes on a finite state-space. Utility is maximised over the class of admissible controls, while Nature chooses a worst-case biometric scenario from the class of admissible, path-dependent cumulative transition rates restricted by path-dependent upper and lower bounds. We prove a martingale optimality principle and a novel existence and uniqueness result for a non-standard worst-case backwards stochastic differential equation, which allows us to establish existence and uniqueness of worst-case and best-case prospective reserves of life and health insurance contracts with reserve-dependent payments. Finally, we find an explicit solution of a novel robust consumption-insurance problem with power utility preferences.

math.OC↗

arXiv2026

Disability insurance with collective health claims: A mean-field approach

The classic semi-Markov disability model is expanded with individual and collective health claims to improve its explanatory and predictive power -- in particular in the context of group experience rating. The inclusion of collective health claims leads to a computationally challenging many-body problem. By adopting a mean-field approach, this many-body problem can be approximated by a non-linear one-body problem, which in turn leads to a transparent pricing method for disability coverages based on a lower-dimensional system of non-linear forward integro-differential equations. In a practice-oriented simulation study, the mean-field approximation clearly stands its ground in comparison to naïve Monte Carlo methods.

q-fin.RM↗

arXiv2026

Mean-field approximations in insurance

The calculation of the insurance liabilities of a cohort of dependent individuals in general requires the solution of a high-dimensional system of coupled linear forward integro-differential equations, which is infeasible for a larger cohort. However, by using a mean-field model, the high dimensional system of linear forward equations can be replaced by a low-dimensional system of non-linear forward integro-differential equations. We show that, subject to certain regularity conditions, the insurance liability viewed as a (conditional) expectation of a functional of an underlying jump process converges to its mean-field counterpart, as the number of individuals in the cohort goes to infinity. Examples from both life- and non-life insurance illuminate the practical importance of mean-field approximations.

q-fin.RM↗