Abstract: The drawdown of a stochastic process is the absolute distance to its running maximum and can be interpreted as a path-dependent measure of risk. In this talk, we consider a stochastic control problem inspired by the real-world question of how to reinsure in an ‘optimal’ way. Here, the notion of optimality is based on the minimisation of the ‘expected time in (critical) drawdown’ under dynamic controls, i.e. the time during which the drawdown process exceeds a predefined, ‘critical’ threshold d > 0. By exploiting connections to Laplace transforms of passage times, Hamilton–Jacobi–Bellman equations, Gerber-Shiu functions and reflected stochastic differential equations, we find the value functions and the optimal strategies for the Cramér-Lundberg and the Brownian risk model.
Stochastic Optimisation of Drawdowns via Dynamic Reinsurance Controls
09.06.2022 17:00 - 17:30
Location:
TU Wien, Freihaus, Gelber Bereich, 10.OG, Seminarraum DB gelb 10, Wiedner Hauptstr. 8, 1040 Wien