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Chance constrained problems: penalty reformulation and performance of sample approximation technique

Martin Branda (2012)

Kybernetika

We explore reformulation of nonlinear stochastic programs with several joint chance constraints by stochastic programs with suitably chosen penalty-type objectives. We show that the two problems are asymptotically equivalent. Simpler cases with one chance constraint and particular penalty functions were studied in [6,11]. The obtained problems with penalties and with a fixed set of feasible solutions are simpler to solve and analyze then the chance constrained programs. We discuss solving both problems...

Compound Compound Poisson Risk Model

Minkova, Leda D. (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 60K10, 62P05.The compound Poisson risk models are widely used in practice. In this paper the counting process in the insurance risk model is a compound Poisson process. The model is called Compound Compound Poisson Risk Model. Some basic properties and ruin probability are given. We analyze the model under the proportional reinsurance. The optimal retention level and the corresponding adjustment coefficient are obtained. The particular case of the Pólya-Aeppli...

Copula-based grouped risk aggregation under mixed operation

Quan Zhou, Zhenlong Chen, Ruixing Ming (2016)

Applications of Mathematics

This paper deals with the problem of risk measurement under mixed operation. For this purpose, we divide the basic risks into several groups based on the actual situation. First, we calculate the bounds for the subsum of every group of basic risks, then we obtain the bounds for the total sum of all the basic risks. For the dependency relationships between the basic risks in every group and all of the subsums, we give different copulas to describe them. The bounds for the aggregated risk under mixed...

Core solutions and nash equilibria in noncooperative games with a measure space of players

Sjur Didrik Flåm, Andrzej Wieczorek (2006)

Banach Center Publications

The paper deals with noncooperative games in which players constitute a measure space. Strategy profiles that are equal almost everywhere are assumed to have the same interactive effects. Under these circumstances we explore links between core solutions and Nash equilibria. Conditions are given which guarantee that core outcomes must be Nash equilibria and vice versa. The main contribution are results on nonemptieness of the core.

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