arXiv subjects

Nils Detering

Publications and source records attributed to Nils Detering.

21 records · Page 2Linked to original sources

arXiv2019

Directed Chain Stochastic Differential Equations

We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain interaction and (ii) a mean-field interaction. It can be approximated by a limit of finite particle systems, as the number of particles goes to infinity. Due to the local chain interaction, propagation of chaos does not necessarily hold. Furthermore, we exhibit a dichotomy of presence or absence of mean-field interaction, and we discuss the problem of detecting its presence from the observation of a single component process.

math.PR↗

arXiv2018

Local risk-minimization with multiple assets under illiquidity with applications in energy markets

We propose a hedging approach for general contingent claims when liquidity is a concern and trading is subject to transaction cost. Multiple assets with different liquidity levels are available for hedging. Our risk criterion targets a tradeoff between minimizing the risk against fluctuations in the stock price and incurring low liquidity costs. Following Çetin U., Jarrow R.A., and Protter P. (2004) we work in an arbitrage-free setting assuming a supply curve for each asset. In discrete time, following the ideas in Schweizer M. (1998) and Lamberton D., Pham H., Schweizer M. (1998) we prove the existence of a locally risk-minimizing strategy under mild conditions on the price process. Under stochastic and time-dependent liquidity risk we give a closed-form solution for an optimal strategy in the case of a linear supply curve model. Finally we show how our hedging method can be applied in energy markets where futures with different maturities are available for trading. The futures closest to their delivery period are usually the most liquid but depending on the contingent claim not necessary optimal in terms of hedging. In a simulation study we investigate this tradeoff and compare the resulting hedge strategies with the classical ones.

q-fin.MF↗

arXiv2017

Bootstrap percolation in directed and inhomogeneous random graphs

Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds that threshold, the vertex gets infected as well and remains so forever. We perform a thorough analysis of bootstrap percolation on a novel model of directed and inhomogeneous random graphs, where the distribution of the edges is specified by assigning two distinct weights to each vertex, describing the tendency of it to receive edges from or to send edges to other vertices. Under the assumption that the limiting degree distribution of the graph is integrable we determine the typical fraction of infected vertices. Our model allows us to study a variety of settings, in particular the prominent case in which the degree distribution has an unbounded variance. Among other results, we quantify the notion of "systemic risk", that is, to what extent local adverse shocks can propagate to large parts of the graph through a cascade, and discover novel features that make graphs prone/resilient to initially small infections.

math.PR↗