arXiv subjects

Lea Enzi

Publications and source records attributed to Lea Enzi.

2 recordsLinked to original sources

arXiv2026

To report or not to report: Optimal claim reporting in a bonus-malus system

We study an optimal claim reporting problem in a bonus-malus setting. We assume, that the insurance contract consists of two regimes, where reporting a claim leads to a transition to a higher-premium regime, whereas remaining claim-free for a prespecified time period results in a shift to the lower premium regime. The insured can decide whether or not to report an occurred claim. We formulate this as an optimal control problem, where the policyholder follows a barrier-type reporting strategy, with the goal of maximizing the expected value of a function of their terminal wealth. We show that the associated value function is the unique viscosity solution to a system of Hamilton-Jacobi-Bellman equations. This characterization allows us to compute numerical approximations of the optimal barrier strategies.

math.OC↗

arXiv2025

Optimal reinsurance in a competitive market

We study a stochastic differential game in a ruin theoretic environment. In our setting two insurers compete for market share, which is represented by a joint performance functional. Consequently, one of the insurers strives to maximize it, while the other seeks to minimize it. As a modelling basis we use classical surplus processes extended by dynamic reinsurance opportunities, which allows us to use techniques from the theory of piecewise deterministic Markov processes to analyze the resulting game. In this context we show that a dynamic programming principle for the upper and lower value of the game holds true and that these values are unique viscosity solutions to the associated Bellman-Isaacs equations. Finally, we provide some numerical illustrations.

math.OC↗