Some statistical estimation problems in ruin theory
نویسنده
چکیده
Much research in ruin theory in insurance mathematics focuses on the behaviour of various quantities of interest, such as the probability of ruin or the ruin-time moments, for a particular risk model in insurance. In practice, precise knowledge of the risk model is available only via observed data. In this presentation, the problem of statistical estimation of the quantities of interest, given data on claim arrivals and claim sizes, is considered. Nonparametric estimators are proposed and their statistical properties are studied. In many cases, the quantities of interest are functions, and this leads to the use of techniques for estimation in function spaces. The bootstrap is used to obtain simultaneous confidence bands for the unknown quantities.
منابع مشابه
Sensitivity Analysis for Ruin Probabilities: Canonical Risk Model
The surplus process of an insurance portfolio is defined as the wealth obtained by the premium payments minus the reimboursements made at the times of claims. When this process becomes negative (if ever), we say that ruin has occurred. The general setting is the Gambler’s Ruin Problem. In this paper we address the problem of estimating derivatives (sensitivities) of ruin probabilities with resp...
متن کاملAn inequality for rational functions with applications to some statistical estimation problems
The well-known Baum-Eagon inequality I31 provides an effective iterative scheme for finding a local maximum for homogeneous polynomials with positive coefticients over a domain of probability values. However, in many applications we are interested in maximizing a general rational function. We extend the Baum-Eagon inequality to rational functions. We briefly describe some of the applications of...
متن کاملFinite Time Ruin Probabilities and Martingales
In this paper we give an introduction to collective risk theory in its simplest form. Our aims are to indicate how some basic facts may be obtained by martingale methods and to point out some open problems
متن کاملLocalized Upper and Lower Bounds for Some Estimation Problems
We derive upper and lower bounds for some statistical estimation problems. The upper bounds are established for the Gibbs algorithm. The lower bounds, applicable for all statistical estimators, match the obtained upper bounds for various problems. Moreover, our framework can be regarded as a natural generalization of the standard minimax framework, in that we allow the performance of the estima...
متن کاملSimulation-based inference for the finite-time ruin probability of a surplus with a long-memory
We are interested in statistical inference for the finite-time ruin probability of an insurance surplus whose claim process has a long-range dependence. As an approximated model, we consider a surplus driven by a fractional Brownian motion with the Hurst parameter H > 1/2. We can compute the ruin probability via the Monte Carlo simulations if some unknown parameters in the model are decided. Fr...
متن کامل