arXiv subjects

Stefan Kremsner

Publications and source records attributed to Stefan Kremsner.

3 recordsLinked to original sources

arXiv2021

Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate

We investigate a dividend maximization problem under stochastic interest rates with Ornstein-Uhlenbeck dynamics. This setup also takes negative rates into account. First a deterministic time is considered, where an explicit separating curve $α(t)$ can be found to determine the optimal strategy at time $t$. In a second setting we introduce a strategy-independent stopping time. The properties and behavior of these optimal control problems in both settings are analyzed in an analytical HJB-driven approach as well as using backward stochastic differential equations.

math.OC↗

arXiv2020

A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics

In insurance mathematics optimal control problems over an infinite time horizon arise when computing risk measures. Their solutions correspond to solutions of deterministic semilinear (degenerate) elliptic partial differential equations. In this paper we propose a deep neural network algorithm for solving such partial differential equations in high dimensions. The algorithm is based on the correspondence of elliptic partial differential equations to backward stochastic differential equations with random terminal time.

q-fin.MF↗

arXiv2020

$L^p$-Solutions and Comparison Results for Lévy Driven BSDEs in a Monotonic, General Growth Setting

We present a unified approach to $L^p$-solutions ($p > 1$) of multidimensional backward stochastic differential equations (BSDEs) driven by Lévy processes and more general filtrations. New existence, uniqueness and comparison results are obtained. The generator functions obey a time-dependent extended monotonicity (Osgood) condition in the $y$-variable and have general growth in $y$. Within this setting, the results generalize those of Royer (2006), Yin and Mao (2008), Yao (2017), Kruse and Popier (2016/2017) and Geiss and Steinicke (2018).

math.PR↗