# A continuous-time theory of reinsurance chains

*Lv Chen*,
*Yang Shen* and
*Jianxi Su*

*Insurance: Mathematics and Economics*, 2020, vol. 95, issue C, 129-146

**Abstract:**
A chain of reinsurance is a hierarchical system formed by the subsequent interactions among multiple (re)insurance agents, which is quite often encountered in practice. This paper proposes a novel continuous-time framework for studying the optimal reinsurance strategies within a chain of reinsurance. The transactions between reinsurance buyers and sellers are formulated by means of Stackelberg games, in order to reflect the conflicting interests and unequal negotiation powers in the bargaining process. Assuming the variance premium principle and the mean–variance criterion on the surplus processes, we solve the time-consistent optimal reinsurance demands and pricing strategies in explicit forms, which are surprisingly plain.

**Keywords:** Stackelberg games; Variance principle; Mean–variance optimization; Time inconsistency; Systemic risk (search for similar items in EconPapers)

**JEL-codes:** C61 G11 G22 (search for similar items in EconPapers)

**Date:** 2020

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:insuma:v:95:y:2020:i:c:p:129-146

**DOI:** 10.1016/j.insmatheco.2020.09.005

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