Related papers: How much is optimal reinsurance degraded by error?
This paper studies an optimal insurance contracting problem in which the preferences of the decision maker given by the sum of the expected loss and a convex, increasing function of a deviation measure. As for the deviation measure, our…
We consider the rate of convergence of the expected loss of empirically optimal vector quantizers. Earlier results show that the mean-squared expected distortion for any fixed distribution supported on a bounded set and satisfying some…
We investigate the optimal reinsurance problem under the criterion of maximizing the expected utility of terminal wealth when the insurance company has restricted information on the loss process. We propose a risk model with claim arrival…
Many insurance premium principles are defined and various estimation procedures introduced in the literature. In this paper, we focus on the estimation of the excess-of-loss reinsurance premium when the risks are randomly right-censored.…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…
The optimal stopping problem for the risk process with interests rates and when claims are covered immediately is considered. An insurance company receives premiums and pays out claims which have occured according to a renewal process and…
In this paper, we examine the effect of background risk on portfolio selection and optimal reinsurance design under the criterion of maximizing the probability of reaching a goal. Following the literature, we adopt dependence uncertainty to…
We analyze the limiting behavior of the risk premium associated with the Pareto optimal risk sharing contract in an infinitely expanding pool of risks under a general class of law-invariant risk measures encompassing rank-dependent utility…
In this paper we consider an optimal investment and reinsurance problem with partially unknown model parameters which are allowed to be learned. The model includes multiple business lines and dependence between them. The aim is to maximize…
We study a reinsurer who faces multiple sources of model uncertainty. The reinsurer offers contracts to $n$ insurers whose claims follow compound Poisson processes representing both idiosyncratic and systemic sources of loss. As the…
Optimization software enables the solution of problems with millions of variables and associated parameters. These parameters are, however, often uncertain and represented with an analytical description of the parameter's distribution or…
A fundamental challenge in machine learning is the choice of a loss as it characterizes our learning task, is minimized in the training phase, and serves as an evaluation criterion for estimators. Proper losses are commonly chosen, ensuring…
In a wide range of statistical learning problems such as ranking, clustering or metric learning among others, the risk is accurately estimated by $U$-statistics of degree $d\geq 1$, i.e. functionals of the training data with low variance…
We consider the optimal risk transfer from an insurance company to a reinsurer. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some crucial distinctions. In…
A variety of optimization problems takes the form of a minimum norm optimization. In this paper, we study the change of optimal values between two incrementally constructed least norm optimization problems, with new measurements included in…
We study prediction and estimation problems using empirical risk minimization, relative to a general convex loss function. We obtain sharp error rates even when concentration is false or is very restricted, for example, in heavy-tailed…
The problems of optimal recovery of unbounded operators are studied. Optimality means the highest possible accuracy and the minimal amount of discrete information involved. It is established that the truncation method, when certain…
Absolute value linear programming problems is quite a new area of optimization problems, involving linear functions and absolute values in the description of the model. In this paper, we consider interval uncertainty of the input…
We study robust linear regression in high-dimension, when both the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\alpha=n/d$, and study a data model that includes outliers. We provide exact asymptotics for the…
We study the problem of robustly estimating the mean of a $d$-dimensional distribution given $N$ examples, where most coordinates of every example may be missing and $\varepsilon N$ examples may be arbitrarily corrupted. Assuming each…