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Optimal stopping of a risk process

100%

Ferenstein E. Z. , Sierociński A.

tom 24

nr 3

335-342

Optimal stopping time problems for a risk process $U_t=u+ct-\sum_{n=0}^{N(t)}X_n$ where the number N(t) of losses up to time t is a general renewal process and the sequence of $X_i$'s represents successive losses are studied. N(t) and $X_i$'s are independent. Our goal is to maximize the expected return before the ruin time. The main results are closely related to those obtained by Boshuizen and Gouweleew [2].

Risk processes with dependent claim size and claim occurrence times

80%

Heilpern S.

nr 10(16)

57-68

The paper is devoted to the risk process, when the claim amount and the interclaim times may be dependent. The impact of the degree of dependence on the probability of ruin is investigated. The three cases are studied: the case when the joint distribution has the bivariate exponential distribution and when the dependent structure is described by FGM and Clayton copulas. The comparison with the previous study is made too.

Dependent discrete risk processes –calculation of the probability of ruin

70%

Heilpern S.

Operations Research and Decisions

2010

tom Vol. 20, No. 2

59-76

This paper is devoted to discrete processes of dependent risks. The random variables describing the time between claims can be dependent in such processes, unlike under the classical approach. The ruin problem is investigated and the probably of ruin is computed. The relation between the degree of dependence and the probability of ruin is studied. Three cases are presented. Different methods of characterizing the dependency structure are examined. First, strictly dependent times between claims are investigated. Next, the dependency structure is described using an Archimedean copula or using Markov chains. In the last case, three situations in which the probability of ruin can be exactly computed are presented. Numerical examples in which the claims have a geometric distribution are investigated. A regular relation between the probability of ruin and the degree of dependence is only observed in the Markov chain case.

Ruin probability in a risk model with variable premium intensity and risky investments

51%

Mishura Y. , Perestyuk M. , Ragulina O.

Opuscula Mathematica

2015

tom Vol. 35, no. 3

333--352

We consider a generalization of the classical risk model when the premium intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of which follows a geometric Brownian motion. We get an exponential bound for the infinite-horizon ruin probability. To this end, we allow the surplus process to explode and investigate the question concerning the probability of explosion of the surplus process between claim arrivals.