Abstract We consider a Hidden Markov Model (HMM) where the integrated continuous-time Markov chain can be observed at discrete time points perturbed by a Brownian motion. The aim is to derive a filter for the underlying continuous-time Markov chain. The recursion formula for the discrete-time...

Abstract The present paper analyzes an optimal consumption and investment problem of a retiree with a constant relative risk aversion (CRRA) who faces parameter uncertainty about the financial market. We solve the optimization problem under partial information by making the market...

Abstract Major events like the COVID-19 crisis have impact both on the financial market and on claim arrival intensities and claim sizes of insurers. Thus, when optimal investment and reinsurance strategies have to be determined, it is important to consider models which reflect this dependence....

Abstract Assume that the surplus process of an insurance company is described by a general Lévy process and that possible dividend pay-outs to shareholders are restricted to random discrete times which are determined by an independent renewal process. Under this setting we show that the optimal...

Abstract We give a unified mathematical framework for reduced-form models for portfolio credit risk and identify properties which lead to positive dependence of default times. Dependence in the default hazard rates is modeled by common macroeconomic factors as well as by inter-obligor links. It...

We consider a periodic risk model with the possibility of investing into a risky asset, given by a geometrical Brownian motion. The aim is to maximize the adjustment coefficient of the risk process. It is shown that the optimal investment strategy only depends on the averaged data of the model...

We consider a discrete time version of the popular optimal dividend payout problem in risk theory. The novel aspect of our approach is that we allow for a risk averse insurer, i.e., instead of maximising the expected discounted dividends until ruin we maximise the expected utility of discounted...

We consider a dynamic mean-risk problem, where the risk constraint is given by the Average Value–at–Risk. As financial market we choose a discrete-time binomial model which allows for explicit solutions. Problems where the risk constraint on the final wealth is replaced by intermediate risk...

We consider the classical Cramér-Lundberg model with dynamic proportional reinsurance and solve the problem of finding the optimal reinsurance strategy which minimizes the expected quadratic distance of the risk reserve to a given benchmark. This result is extended to a mean-variance problem....