*Tid:***24 oktober 2003 kl 1015-1200 ** (OBS! Tiden)

*Plats :***Stora seminarierummet 3721**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!

*Föredragshållare:***
Hanspeter Schmidli,
Försäkringsmatematiskt laboratorium,
Köpenhamns universitet.
**

**Titel:** **
Asymptotics of ruin probabilities for controlled risk processes.
**

**Sammanfattning:**

We consider a classical risk model with the possibility of reinsurance and investment into a risky asset. The insurer follows the optimal strategy, as found by Hipp and Plum (2000) and Schmidli (2001, 2002). We find the Cramér-Lundberg approximation in the small claim case as well as in the case where no exponential moments exist. In particular we find an exponential decay of the ruin probability by following the optimal strategy. If a fixed part would be invested the ruin probability would have a power tail. We prove that the optimal strategy converges to the strategy maximising the adjustment coefficient as the capital increases to infinity.