On 1-convexity and nucleolus of co-insurance games

Theo S.H. Driessen; Vito Fragnelli; Ilya V. Katsev; Anna B. Khmelnitskaya

doi:10.1016/j.insmatheco.2010.10.009

On 1-convexity and nucleolus of co-insurance games

Theo S.H. Driessen
, Vito Fragnelli
, Ilya V. Katsev
, Anna B. Khmelnitskaya

Research output: Contribution to journal › Article › peer-review

Abstract

The insurance situation in which an enormous risk is insured by a number of insurance companies is modeled through a cooperative TU game, the so-called co-insurance game, first introduced in Fragnelli and Marina (2004). In this paper we present certain conditions on the parameters of the model that guarantee the 1-convexity property of co-insurance games which in turn ensures the nonemptiness of the core and the linearity of the nucleolus as a function of the variable premium. Further we reveal conditions when a co-insurance game is representable in the form of a veto-removed game and present an efficient final algorithm for computing the nucleolus of a veto-removed game.

Original language	English
Pages (from-to)	217-225
Number of pages	9
Journal	Insurance: Mathematics and Economics
Volume	48
Issue number	2
DOIs	https://doi.org/10.1016/j.insmatheco.2010.10.009
Publication status	Published - Mar 2011
Externally published	Yes

Keywords

Cooperative game
Core
Insurance situation
Nucleolus

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10.1016/j.insmatheco.2010.10.009

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title = "On 1-convexity and nucleolus of co-insurance games",

abstract = "The insurance situation in which an enormous risk is insured by a number of insurance companies is modeled through a cooperative TU game, the so-called co-insurance game, first introduced in Fragnelli and Marina (2004). In this paper we present certain conditions on the parameters of the model that guarantee the 1-convexity property of co-insurance games which in turn ensures the nonemptiness of the core and the linearity of the nucleolus as a function of the variable premium. Further we reveal conditions when a co-insurance game is representable in the form of a veto-removed game and present an efficient final algorithm for computing the nucleolus of a veto-removed game.",

keywords = "Cooperative game, Core, Insurance situation, Nucleolus",

author = "Driessen, \{Theo S.H.\} and Vito Fragnelli and Katsev, \{Ilya V.\} and Khmelnitskaya, \{Anna B.\}",

note = "Funding Information: The research of Theo Driessen, Ilya Katsev, and Anna Khmelnitskaya was supported by NWO (The Netherlands Organization for Scientific Research) grant NL-RF 047.017.017 . The research of Ilya Katsev was also supported by RFBR (Russian Foundation for Basic Research) grant 09-06-00155 . The research was partially done in 2008 during Anna Khmelnitskaya{\textquoteright}s research stay at the Tilburg Center for Logic and Philosophy of Science (TiLPS, Tilburg University) whose hospitality and support are highly appreciated as well. ",

year = "2011",

month = mar,

doi = "10.1016/j.insmatheco.2010.10.009",

language = "English",

volume = "48",

pages = "217--225",

journal = "Insurance: Mathematics and Economics",

issn = "0167-6687",

publisher = "Elsevier BV",

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AU - Driessen, Theo S.H.

AU - Fragnelli, Vito

AU - Katsev, Ilya V.

AU - Khmelnitskaya, Anna B.

N1 - Funding Information: The research of Theo Driessen, Ilya Katsev, and Anna Khmelnitskaya was supported by NWO (The Netherlands Organization for Scientific Research) grant NL-RF 047.017.017 . The research of Ilya Katsev was also supported by RFBR (Russian Foundation for Basic Research) grant 09-06-00155 . The research was partially done in 2008 during Anna Khmelnitskaya’s research stay at the Tilburg Center for Logic and Philosophy of Science (TiLPS, Tilburg University) whose hospitality and support are highly appreciated as well.

PY - 2011/3

Y1 - 2011/3

N2 - The insurance situation in which an enormous risk is insured by a number of insurance companies is modeled through a cooperative TU game, the so-called co-insurance game, first introduced in Fragnelli and Marina (2004). In this paper we present certain conditions on the parameters of the model that guarantee the 1-convexity property of co-insurance games which in turn ensures the nonemptiness of the core and the linearity of the nucleolus as a function of the variable premium. Further we reveal conditions when a co-insurance game is representable in the form of a veto-removed game and present an efficient final algorithm for computing the nucleolus of a veto-removed game.

AB - The insurance situation in which an enormous risk is insured by a number of insurance companies is modeled through a cooperative TU game, the so-called co-insurance game, first introduced in Fragnelli and Marina (2004). In this paper we present certain conditions on the parameters of the model that guarantee the 1-convexity property of co-insurance games which in turn ensures the nonemptiness of the core and the linearity of the nucleolus as a function of the variable premium. Further we reveal conditions when a co-insurance game is representable in the form of a veto-removed game and present an efficient final algorithm for computing the nucleolus of a veto-removed game.

KW - Cooperative game

KW - Core

KW - Insurance situation

KW - Nucleolus

UR - https://www.scopus.com/pages/publications/78649538827

U2 - 10.1016/j.insmatheco.2010.10.009

DO - 10.1016/j.insmatheco.2010.10.009

M3 - Article

SN - 0167-6687

VL - 48

SP - 217

EP - 225

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

IS - 2

ER -

On 1-convexity and nucleolus of co-insurance games

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Keywords

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