arXiv subjects

Nils Engler

Publications and source records attributed to Nils Engler.

5 recordsLinked to original sources

arXiv2026

Outrunning the Omega Clock: A Singular Control Problem for Dividend Optimisation with Ruin and Time-in-Distress Default

This paper extends the classical dividend problem by incorporating a novel, path-dependent mechanism of firm default. In the traditional framework, ruin occurs when the surplus process first reaches zero. In contrast, default in our model may also arise when the surplus spends an excessive amount of time below a distress threshold, even without ever hitting zero. This occupation-time-based default criterion captures financial distress more realistically, as prolonged periods of low liquidity or capitalisation may trigger regulatory intervention or operational failure. The resulting optimisation problem is formulated as a new singular stochastic control problem with discontinuous state-dependent discounting and killing. We provide a complete analytical solution via a bespoke sequential guess-and-verify method and identify three distinct classes of optimal dividend strategies corresponding to different parameter regimes of the dual-ruin structure. Notably, for certain distress thresholds, the optimal policy features disconnected action and inaction regions. We further show that, unlike in the classical dividend problem, higher effective discounting induced by occupation time below a distress level can lead to delayed, rather than earlier, dividend payments.

math.OC↗

arXiv2025

Regularisation of CART trees by summation of $p$-values

The standard procedure to decide on the complexity of a CART regression tree is to use cross-validation with the aim of obtaining a predictor that generalises well to unseen data. The randomness in the selection of folds implies that the selected CART regression tree is not a deterministic function of the data. Moreover, the cross-validation procedure may become time consuming and result in inefficient use of training data. We propose a simple deterministic in-sample method that can be used for stopping the growing of a CART regression tree based on node-wise statistical tests. This testing procedure is derived using a connection to change point detection, where the null hypothesis corresponds to no signal. The suggested $p$-value based procedure allows us to consider covariate vectors of arbitrary dimension and allows us to bound the $p$-value of an entire tree from above. Further, we show that the test detects a not too weak signal with a high probability, given a not too small sample size. We illustrate our methodology and the asymptotic results on both simulated and real world data. Additionally, we illustrate how the $p$-value based method can be used to construct a deterministic piece-wise constant auto-calibrated predictor based on a given black-box predictor.

stat.ME↗

arXiv2023

Mack's estimator motivated by large exposure asymptotics in a compound Poisson setting

The distribution-free chain ladder of Mack justified the use of the chain ladder predictor and enabled Mack to derive an estimator of conditional mean squared error of prediction for the chain ladder predictor. Classical insurance loss models, i.e. of compound Poisson type, are not consistent with Mack's distribution-free chain ladder. However, for a sequence of compound Poisson loss models indexed by exposure (e.g. number of contracts), we show that the chain ladder predictor and Mack's estimator of conditional mean squared error of prediction can be derived by considering large exposure asymptotics. Hence, quantifying chain ladder prediction uncertainty can be done with Mack's estimator without relying on the validity of the model assumptions of the distribution-free chain ladder.

q-fin.RM↗

arXiv2023

Approximations of multi-period liability values by simple formulas

This paper is motivated by computational challenges arising in multi-period valuation in insurance. Aggregate insurance liability cashflows typically correspond to stochastic payments several years into the future. However, insurance regulation requires that capital requirements are computed for a one-year horizon, by considering cashflows during the year and end-of-year liability values. This implies that liability values must be computed recursively, backwards in time, starting from the year of the most distant liability payments. Solving such backward recursions with paper and pen is rarely possible, and numerical solutions give rise to major computational challenges. The aim of this paper is to provide explicit and easily computable expressions for multi-period valuations that appear as limit objects for a sequence of multi-period models that converge in terms of conditional weak convergence. Such convergence appears naturally if we consider large insurance portfolios such that the liability cashflows, appropriately centered and scaled, converge weakly as the size of the portfolio tends to infinity.

econ.GN↗

arXiv2022

Gibbsianness of locally thinned random fields

We consider the locally thinned Bernoulli field on $\mathbb Z^d$, which is the lattice version of the Type-I Mat\'ern hardcore process in Euclidean space. It is given as the lattice field of occupation variables, obtained as image of an i.i.d. Bernoulli lattice field with occupation probability $p$, under the map which removes all particles with neighbors, while keeping the isolated particles. We prove that the thinned measure has a Gibbsian representation and provide control on its quasilocal dependence, both in the regime of small $p$, but also in the regime of large $p$, where the thinning transformation changes the Bernoulli measure drastically. Our methods rely on Dobrushin uniqueness criteria, disagreement percolation arguments, and cluster expansions.

math.PR↗