arXiv subjects
Publications and source records attributed to Sebastian Baran.
We find the asymptotics of the value function maximizing the expected utility of discounted dividend payments of an insurance company whose reserves are modeled as a classical Cram\'er risk process, with exponentially distributed claims, when the initial reserves tend to infinity. We focus on the power and logarithmic utility functions. We perform some numerical analysis as well.
The insurance industry, with its large datasets, is a natural place to use big data solutions. However it must be stressed, that significant number of applications for machine learning in insurance industry, like fraud detection or claim prediction, deals with the problem of machine learning on an imbalanced data set. This is due to the fact that frauds or claims are rare events when compared with the entire population of drivers. The problem of imbalanced learning is often hard to overcome. Therefore, the main goal of this work is to present and apply various methods of dealing with an imbalanced dataset in the context of claim occurrence prediction in car insurance. In addition, the above techniques are used to compare the results of machine learning algorithms in the context of claim occurrence prediction in car insurance. Our study covers the following techniques: logistic-regression, decision tree, random forest, xgBoost, feed-forward network. The problem is the classification one.
We consider the problem of maximizing the discounted utility of dividend payments of an insurance company whose reserves are modeled as a classical Cram\'er-Lundberg risk process. We investigate this optimization problem under the constraint that dividend rate is bounded. We prove that the value function fulfills the Hamilton-Jacobi-Bellman equation and we identify the optimal dividend strategy.