*Tid:* **28 oktober 2013 kl 15.15-16.00.**
**Seminarierummet 3721**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7.
Karta!
*Föredragshållare:*
**
Professor Hanspeter
Schmidli, Institute of Mathematics,
University of Cologne.
**
**Titel:**
Optimal Dividends and Capital Injection Problems in Non-Life Insurance
**Abstract**
The traditional risk measure in actuarial mathematics is the ruin
probability. This concept has been criticised because it does not take into
account the time of ruin and the deficit at ruin. An alternative measure has
been suggested by de Finetti (1957). He proposed to consider the discounted
value of dividends paid from the portfolio. However, under the optimal
dividend strategy ruin becomes certain. Moreover, the deficit at ruin is not
taken into account, either. Moreover, ruin is certain under the optimal
dividend strategy.
As an alternative, we allow capital injections that should keep the surplus
positive. Ruin is not allowed in our model. In one model, we measure the risk
as the value of the (discounted) capital injections. We look for the
reinsurance strategy that minimises the value. A second model allows
also dividend payments. Here, the value is the discounted dividends minus
penalised capital injections. We show that the optimal dividend strategy is a
barrier strategy.
This talk is based on joint work with Julia Eisenberg and Natalie Scheer.
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