Das Institut für Mathematische Wirtschaftsforschung veranstaltet im Rahmen des Bielefeld Stochastic Afternoon regelmäßig Seminare zum Thema Finanzmathematik. Das Programm des aktuellen Semesters finden Sie hier.
Giovanni Alessandro Zanco (Università di Siena)
Titel: Control of age-structured models of epidemic-economics dynamics
Abstract: We first introduce SIR-type dynamics in the presence of an age-structure, that is, taking into account possible dependence of coefficients and solutions on the age of individuals. We then discuss possible stochastic extensions in this setting. Coupling the SIR dynamics with economic dynamics we formulate a control problem for a planner who has to balance the mitigation of the epidemic diffusion with its effects on the economy. For this problem In this setting we present some verification results for the Hamilton-Jacobi-Bellman equation of the control problem. The presentation is based on joint work with Giorgio Fabbri and Fausto Gozzi.
Marcus C. Christiansen (Universität Oldenburg)
Titel: Decomposition of profits and losses in dynamic time
Abstract: Profit and loss attribution has a long history in risk management. It is the process of analyzing the change between two valuation dates and explaining the development of profits and losses by the movement of the risk sources between the two dates. The presentation starts with time-discrete modelling and discusses axiomatic concepts as well as heuristic methods for generating profit and loss decompositions. The concepts are then generalized to time-continuous modelling and a unique decomposition principle is identified through nine axioms. The theoretical results are illustrated with examples from insurance and finance.