Work

Optimal Policies in an Insurance Stackelberg Game: Demand Response and Premium Setting

Year: 2026

Type: article

Abstract: This paper examines a stochastic Stackelberg differential game between an insurer and a pool of homogeneous policyholders. Policyholders dynamically optimize insurance coverage and risky asset allocations to minimize the probability of wealth shortfall, while the insurer, acting as the leader, sets the premium loading to maximize the expected exponential utility of terminal surplus. Employing dynamic programming techniques, we derive closed-form equilibrium strategies for both parties. The analysis reveals that a strong positive correlation between insurance claims and financial market returns incentivizes full coverage with modest premiums, whereas a strong negative correlation may induce market collapse as insurers exit underwriting to exploit natural hedging opportunities. Furthermore, larger policyholder pools generate diversification benefits that reduce equilibrium premiums and stimulate insurance demand.

Source: Mathematics

DOI: 10.3390/math14020370

Authors: Cuixia Chen, Bing Liu, Fumei He, Darhan Bahtbek

Institutions: Hebei Finance University, Nanjing University of Finance and Economics

Language: English

Topic: Probability and Risk Models

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: National Social Science Fund of China