arXiv subjects

Thomas Knispel

Publications and source records attributed to Thomas Knispel.

4 recordsLinked to original sources

arXiv2022

Modeling and Pricing Cyber Insurance -- Idiosyncratic, Systematic, and Systemic Risks

The paper provides a comprehensive overview of modeling and pricing cyber insurance and includes clear and easily understandable explanations of the underlying mathematical concepts. We distinguish three main types of cyber risks: idiosyncratic, systematic, and systemic cyber risks. While for idiosyncratic and systematic cyber risks, classical actuarial and financial mathematics appear to be well-suited, systemic cyber risks require more sophisticated approaches that capture both network and strategic interactions. In the context of pricing cyber insurance policies, issues of interdependence arise for both systematic and systemic cyber risks; classical actuarial valuation needs to be extended to include more complex methods, such as concepts of risk-neutral valuation and (set-valued) monetary risk measures.

q-fin.RM↗

arXiv2021

Asymptotic Analysis of Risk Premia Under Linear Risk Sharing with Law-Invariant Risk Measures

We investigate the asymptotic behavior of the risk premium associated with a linear risk sharing contract in an infinitely expanding risk pool. We consider general preferences represented by law-invariant robust utility functionals. These preferences encompass the rank-dependent utility model as a special case. We also examine Pareto optimality of general and, in particular, linear risk sharing rules with these preferences. Our analysis is not limited to the classical i.i.d. setting, but allows for heterogeneous risks. Two case studies on actuarial pricing for independent but heterogeneous risks illustrate our results.

q-fin.RM↗

arXiv2016

Robust Optimal Risk Sharing and Risk Premia in Expanding Pools

We consider the problem of optimal risk sharing in a pool of cooperative agents. We analyze the asymptotic behavior of the certainty equivalents and risk premia associated with the Pareto optimal risk sharing contract as the pool expands. We first study this problem under expected utility preferences with an objectively or subjectively given probabilistic model. Next, we develop a robust approach by explicitly taking uncertainty about the probabilistic model (ambiguity) into account. The resulting robust certainty equivalents and risk premia compound risk and ambiguity aversion. We provide explicit results on their limits and rates of convergence, induced by Pareto optimal risk sharing in expanding pools.

q-fin.RM↗

arXiv2012

Asymptotics of robust utility maximization

For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $λ\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.

math.PR↗