# Risk-adjusted Bowley reinsurance under distorted probabilities

*Ka Chun Cheung*,
*Sheung Chi Phillip Yam* and
*Yiying Zhang*

*Insurance: Mathematics and Economics*, 2019, vol. 86, issue C, 64-72

**Abstract:**
In the seminal work of Chan and Gerber (1985), one of the earliest game theoretical approaches was proposed to model the interaction between the reinsurer and insurer; in particular, the optimal pricing density for the reinsurer and optimal ceded loss for the insurer were determined so that their corresponding expected utilities could be maximized. Over decades, their advocated Bowley solution (could be understood as Stackelberg equilibria) concept of equilibrium reinsurance strategy has not been revisited in the modern risk management framework. In this article, we attempt to fill this gap by extending their work to the setting of general premium principle for the reinsurer and distortion risk measure for the insurer.

**Keywords:** Bowley solution; Stackelberg equilibria; Equilibrium reinsurance strategy; Pricing density; General premium principle; Distortion risk measure; Tail Value-at-Risk; Value-at-Risk (search for similar items in EconPapers)

**JEL-codes:** C61 G22 G32 (search for similar items in EconPapers)

**Date:** 2019

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** View citations in EconPapers (1) Track citations by RSS feed

**Downloads:** (external link)

http://www.sciencedirect.com/science/article/pii/S0167668718301963

Full text for ScienceDirect subscribers only

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:eee:insuma:v:86:y:2019:i:c:p:64-72

**DOI:** 10.1016/j.insmatheco.2019.02.006

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by *R. Kaas*, *Hansjoerg Albrecher*, *M. J. Goovaerts* and *E. S. W. Shiu*

More articles in Insurance: Mathematics and Economics from Elsevier

Bibliographic data for series maintained by Haili He ().