Oberseminar Stochastik
Thema: The challenge of a negative interest rate in non-life insurance. Referent: Dr. Julia Eisenberg, TU Wien, Freitag, 27.05.2016, Raum: ENC D-223, Zeit: 13:00 Uhr
Oberseminar Stochastik
The challenge of a negative interest rate in non-life insurance.
Freitag, den 27.05.2016, um 13:00 Uhr, im
Raum ENC D-223,
Referent: Dr. Julia Eisenberg, (TU Wien)
Abstrakt:
In this talk we consider some models incorporating a
stochastic interest rate. First we consider an individual
or household endowed with an initial capital and an income,
modeled as a linear function of time. The discounting
function is given by a stochastic process, where the short
rate evolves due an Ornstein-Uhlenbeck process. The target
is to find an unrestricted consumption strategy such that
the value of the expected discounted consumption is
maximized. Due to a complex structure of the first hitting
times of an Ornstein- Uhlenbeck process with drift, we
cannot find an explicit expression for the value function.
However, it is possible to describe the value function via
several ODEs corresponding to different initial value
regions. Also, we prove the optimal strategy to be of a
barrier type. In the second part, we consider an insurance
entity endowed with an initial capital and an income,
modeled as a Brownian motion with drift. It is assumed that
the insurance company seeks to maximise the cumulated value
of expected discounted dividends up to the ruin time under
the assumption of a) a geometric Brownian motion as a
discounting factor, b) an Onstein-Uhlenbeck process as an
interest rate. In the geometric Brownian motion case, the
optimal strategy turns out to be a constant barrier. In the
case of Vasicek model, it is intuitively clear that the
optimal strategy should be of a non-linear barrier type.
But that's exactly why we cannot apply the classical
verification methods and have to rely on the viscosity
ansatz.
Wir laden alle Interessenten herzlich zum Vortrag ein.