Abstract
The purpose of this article is to consider a two firms excess-loss reinsurance problem. The first firm is defined as the direct underwriter while the second firm is the reinsurer. As in the classical model of collective risk theory it is assumed that premium payments are received deterministically from policyholders at a constant rate, while the claim process is determined by a compound Poisson process. The objective of the underwriter is to maximize the expected present value of the long run terminal wealth (investments plus cash) of the firm by selecting an appropriate excess-loss coverage strategy, while the reinsurer seeks to maximize its total expected discounted profit by selecting an optimal loading factor. Since both firms' policies are interdependent we define an insurance game, solved by employing a Stackelberg solution concept. A diffusion approximation is used in order to obtain tractable results for a general claim size distribution. Finally, an example is presented illustrating computational procedures.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 85-96 |
| Number of pages | 12 |
| Journal | Stochastic Processes and their Applications |
| Volume | 12 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1981 |
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Keywords
- diffusion approximation
- excess-loss
- loading factor
- Reinsurance
- Stackelberge solution
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Mathematics(all)
- Modeling and Simulation
- Statistics and Probability
Cite this
Optimum excess-loss reinsurance : a dynamic framework. / Tapiero, Charles; Zuckerman, Dror.
In: Stochastic Processes and their Applications, Vol. 12, No. 1, 1981, p. 85-96.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Optimum excess-loss reinsurance
T2 - a dynamic framework
AU - Tapiero, Charles
AU - Zuckerman, Dror
PY - 1981
Y1 - 1981
N2 - The purpose of this article is to consider a two firms excess-loss reinsurance problem. The first firm is defined as the direct underwriter while the second firm is the reinsurer. As in the classical model of collective risk theory it is assumed that premium payments are received deterministically from policyholders at a constant rate, while the claim process is determined by a compound Poisson process. The objective of the underwriter is to maximize the expected present value of the long run terminal wealth (investments plus cash) of the firm by selecting an appropriate excess-loss coverage strategy, while the reinsurer seeks to maximize its total expected discounted profit by selecting an optimal loading factor. Since both firms' policies are interdependent we define an insurance game, solved by employing a Stackelberg solution concept. A diffusion approximation is used in order to obtain tractable results for a general claim size distribution. Finally, an example is presented illustrating computational procedures.
AB - The purpose of this article is to consider a two firms excess-loss reinsurance problem. The first firm is defined as the direct underwriter while the second firm is the reinsurer. As in the classical model of collective risk theory it is assumed that premium payments are received deterministically from policyholders at a constant rate, while the claim process is determined by a compound Poisson process. The objective of the underwriter is to maximize the expected present value of the long run terminal wealth (investments plus cash) of the firm by selecting an appropriate excess-loss coverage strategy, while the reinsurer seeks to maximize its total expected discounted profit by selecting an optimal loading factor. Since both firms' policies are interdependent we define an insurance game, solved by employing a Stackelberg solution concept. A diffusion approximation is used in order to obtain tractable results for a general claim size distribution. Finally, an example is presented illustrating computational procedures.
KW - diffusion approximation
KW - excess-loss
KW - loading factor
KW - Reinsurance
KW - Stackelberge solution
UR - http://www.scopus.com/inward/record.url?scp=49049152845&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=49049152845&partnerID=8YFLogxK
U2 - 10.1016/0304-4149(81)90013-2
DO - 10.1016/0304-4149(81)90013-2
M3 - Article
AN - SCOPUS:49049152845
VL - 12
SP - 85
EP - 96
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 1
ER -