منابع مشابه
Some statistical estimation problems in ruin theory
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 ...
متن کاملThe Pólya-aeppli Process and Ruin Problems
The Pólya-Aeppli process as a generalization of the homogeneous Poisson process is defined. We consider the risk model in which the counting process is the Pólya-Aeppli process. It is called a Pólya-Aeppli risk model. The problem of finding the ruin probability and the Cramér-Lundberg approximation is studied. The Cramér condition and the Lundberg exponent are defined. Finally, the comparison b...
متن کاملGeneralized ruin problems and asynchronous random walks
We consider a gambling game with two different kinds of trials and compute the duration of the game (averaged over all possible initial capitals of the players) by a mapping of the problem to a 1D lattice walk of two particles reacting upon encounter. The relative frequency of the trials is governed by the synchronicity parameter p of the random walk. The duration of the game is given by the me...
متن کاملLattice Rules for the Simulation of Ruin Problems
Lattice rules are a quasi-Monte Carlo method, an alternative to the Monte Carlo method for multidimensional numerical integration. The measures of performance that we estimate by simulation can be seen as the values of integrals in large dimensions. Therefore, instead of the usual Monte Carlo method, one can use lattice rules in simulation. In this paper, we compare these rules to the Monte Car...
متن کاملFinite time ruin problems for the Markov-modulated risk model
We consider finite time ruin problems in the Markov-modulated risk model. We start by considering the number of claims and the aggregate claim amount over a finite time interval, in each case giving both a general approach for an arbitrary number of environment states and a specific approach for the special case when the number of environment states is two. We then consider the density of the t...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1977
ISSN: 0304-4149
DOI: 10.1016/0304-4149(77)90051-5