Matstat seminarium fredagen 6 april kl. 13.15 i MH227

Hanspeter Schmidli, Försäkringsmatematisk Laboratorium, Köpenhamn

On minimising the ruin probability by investment and reinsurance

We consider a classical risk model and allow investment into a risky asset
modelled as a Black-Scholes model as well as (proportional) reinsurance. Via
the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal
strategy. We prove a verification theorem in order to show that any increasing
solution to the HJB equation is bounded and solves the optimisation
problem. Finally we prove that an increasing solution to the HJB equation
exists.