Stackelberg differential game for insurance under model ambiguity

Jingyi Cao, Dongchen Li, Virginia R. Young and Bin Zou

Insurance: Mathematics and Economics, 2022, vol. 106, issue C, 128-145

Abstract: We study a dynamic Stackelberg differential game between a buyer and a seller of insurance policies in a spectrally negative Lévy framework, in which both parties are ambiguous about the intensity and severity of insurable losses. Both the buyer and seller aim to maximize their expected wealth, plus a penalty term that reflects ambiguity, over an exogenous random horizon. Under a mean-variance premium principle and a quadratic penalty for ambiguity, we obtain the equilibrium in closed form. Our main results show that the buyer's robust optimal indemnity is a coinsurance with proportion less than one-half, which increases (resp. decreases) as the buyer (resp. seller) becomes more ambiguity averse. Also we show that the seller's robust optimal premium rule equals the net premium under the buyer's optimally distorted probability, which is the buyer's “best hope,” and it exceeds the actuarially fair premium under the seller's optimally distorted probability measure so is, thereby, acceptable to the seller.

Keywords: Stackelberg differential game; Insurance; Ambiguity; Mean-variance premium principle; Random time horizon (search for similar items in EconPapers)
JEL-codes: C61 C72 C73 D81 G22 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:106:y:2022:i:c:p:128-145

DOI: 10.1016/j.insmatheco.2022.06.003

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