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.

Aktualisiert via XIMS am 12.5.2016