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Optimal stochastic control of a path-dependent risk indicator for insurance companies

Leonie Violetta Brinker

Tuesday, 2022-01-18 08:30

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 is a risk and performance measure widely used in financial applications: whilst large and long- lasting drawdowns might manifest existing financial and reputational risks, small and infrequent drawdowns can be considered a sign of economic strength and stability. For this reason, minimising drawdowns is desirable for companies - especially in insurance, where customer trust is the basis for success. In this talk, we consider a stochastic control problem inspired by the minimisation of the drawdown size and "recovery time" for insurance companies. By exploiting connections to Laplace transforms of passage times, Hamilton-Jacobi-Bellman equations and reflected stochastic differential equations, we find value functions and optimal strategies. We discuss our results and implications of the model in explicit examples.