Optimal dividends for a NatCat insurer in the presence of a climate tipping point

Abstract We study optimal dividend strategies for an insurance company facing natural catastrophe claims, anticipating the arrival of a climate tipping point after which the claim intensity and/or the claim size distribution of the underlying risks deteriorates irreversibly. For shot‐noise Cox claim arrivals, we show that the nonstationary feature of such a tipping point can be an advantage for shareholders. Assuming the tipping point arrives according to an Erlang distribution, we demonstrate that the corresponding system of two‐dimensional stochastic control problems admits a viscosity solution, which can be numerically approximated in an efficient way. The results are illustrated through several numerical examples. Also, the sensitivity of the optimal dividend strategies to the presence of a climate tipping point is analyzed.