The optimal claiming strategies in a bonus-malus system and the monotony property

Yaniv Zaks

doi:10.1080/03461230701722869

The optimal claiming strategies in a bonus-malus system and the monotony property

Yaniv Zaks

Department of Mathematics

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

Abstract

In the classical Bonus-Malus System (BMS) there are several premium levels, e.g., M. A premium level i consists of a premium (π_i) and a deductible (d_i). In this paper, we consider the expected cost for a horizon of n periods of a policyholder in level i. This expectation is denoted by E_n(i). When damage of size x occurs, the policyholder should decide whether or not to claim. The minimum damage for which the policyholder will claim should be the solution of min d_i ≤x{x + E_n-1(i- 1); d_i + E_n-1(i+ 1)}: We will show that E_n-1(i-1) ≤ E_n-1(i+1), hence x =di+E_n-1(i +1) -E_n-1(i -1), is a valid solution.

Original language	English
Pages (from-to)	34-40
Number of pages	7
Journal	Scandinavian Actuarial Journal
Issue number	1
DOIs	https://doi.org/10.1080/03461230701722869
State	Published - 2008

Bibliographical note

Funding Information:
I wish to thank Professor S. Zacks for his remarks and encouragement. This research was supported by the Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel, and The Actuarial Research Center at the University of Haifa, Israel.

Funding

I wish to thank Professor S. Zacks for his remarks and encouragement. This research was supported by the Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel, and The Actuarial Research Center at the University of Haifa, Israel.

Funders	Funder number
University of Haifa, Israel
Department of Mathematics, Bar-Ilan University

Keywords

Optimal strategy
Policyholder's behavior

Access to Document

10.1080/03461230701722869

Cite this

@article{1956245810b24b46acf9df5f87247266,

title = "The optimal claiming strategies in a bonus-malus system and the monotony property",

abstract = "In the classical Bonus-Malus System (BMS) there are several premium levels, e.g., M. A premium level i consists of a premium (πi) and a deductible (di). In this paper, we consider the expected cost for a horizon of n periods of a policyholder in level i. This expectation is denoted by En(i). When damage of size x occurs, the policyholder should decide whether or not to claim. The minimum damage for which the policyholder will claim should be the solution of min di ≤x{x + En-1(i- 1); di + En-1(i+ 1)}: We will show that En-1(i-1) ≤ En-1(i+1), hence x =di+En-1(i +1) -En-1(i -1), is a valid solution.",

keywords = "Optimal strategy, Policyholder's behavior",

author = "Yaniv Zaks",

note = "Funding Information: I wish to thank Professor S. Zacks for his remarks and encouragement. This research was supported by the Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel, and The Actuarial Research Center at the University of Haifa, Israel.",

year = "2008",

doi = "10.1080/03461230701722869",

language = "אנגלית",

pages = "34--40",

journal = "Scandinavian Actuarial Journal",

issn = "0346-1238",

publisher = "Taylor and Francis Ltd.",

number = "1",

}

TY - JOUR

T1 - The optimal claiming strategies in a bonus-malus system and the monotony property

AU - Zaks, Yaniv

N1 - Funding Information: I wish to thank Professor S. Zacks for his remarks and encouragement. This research was supported by the Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel, and The Actuarial Research Center at the University of Haifa, Israel.

PY - 2008

Y1 - 2008

N2 - In the classical Bonus-Malus System (BMS) there are several premium levels, e.g., M. A premium level i consists of a premium (πi) and a deductible (di). In this paper, we consider the expected cost for a horizon of n periods of a policyholder in level i. This expectation is denoted by En(i). When damage of size x occurs, the policyholder should decide whether or not to claim. The minimum damage for which the policyholder will claim should be the solution of min di ≤x{x + En-1(i- 1); di + En-1(i+ 1)}: We will show that En-1(i-1) ≤ En-1(i+1), hence x =di+En-1(i +1) -En-1(i -1), is a valid solution.

AB - In the classical Bonus-Malus System (BMS) there are several premium levels, e.g., M. A premium level i consists of a premium (πi) and a deductible (di). In this paper, we consider the expected cost for a horizon of n periods of a policyholder in level i. This expectation is denoted by En(i). When damage of size x occurs, the policyholder should decide whether or not to claim. The minimum damage for which the policyholder will claim should be the solution of min di ≤x{x + En-1(i- 1); di + En-1(i+ 1)}: We will show that En-1(i-1) ≤ En-1(i+1), hence x =di+En-1(i +1) -En-1(i -1), is a valid solution.

KW - Optimal strategy

KW - Policyholder's behavior

UR - http://www.scopus.com/inward/record.url?scp=70350322028&partnerID=8YFLogxK

U2 - 10.1080/03461230701722869

DO - 10.1080/03461230701722869

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:70350322028

SN - 0346-1238

SP - 34

EP - 40

JO - Scandinavian Actuarial Journal

JF - Scandinavian Actuarial Journal

IS - 1

ER -

The optimal claiming strategies in a bonus-malus system and the monotony property

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this