Leonie Violetta Brinker:
Optimal stochastic control of a path-dependent risk indicator for insurance companies
Time and place
Tuesday, 18.1.22, 08:30-09:30, Zoom Meeting
Abstract
The drawdown of a stochastic process (modelling the surplus of a company) is the absolute distance to its historical high water mark. It can therefore be interpreted as a "relative loss" and\nis a risk and performance measure widely used in financial applications: whilst large and long-\nlasting drawdowns might manifest existing financial and reputational risks, small and infrequent\ndrawdowns can be considered a sign of economic strength and stability. For this reason,\nminimising drawdowns is desirable for companies - especially in insurance, where customer trust\nis the basis for success. In this talk, we consider a stochastic control problem inspired by the\nminimisation of the drawdown size and "recovery time" for insurance companies. By exploiting\nconnections to Laplace transforms of passage times, Hamilton-Jacobi-Bellman equations and\nreflected stochastic differential equations, we find value functions and optimal strategies. We\ndiscuss our results and implications of the model in explicit examples.