Demand-based pricing in multiline insurance: a Lévy-copula approach

Nonlife insurance lines often exhibit strong interdependencies due to systemic risks, affecting pricing, reserving, and capital allocation. This paper examines optimal premium setting for a multiline insurer under demand-based pricing, incorporating dependence structures by integrating Lévy copulas into a stochastic optimization framework in which a risk-averse insurer maximizes the expected discounted lifetime utility of consumption. The insurer is a monopolistic price setter that influences demand and claim arrival rates through premium adjustments. The optimization problem resembles a multiproduct monopolist with a nonseparable cost function driven by claim dependence. For the case of two-line insurers, we establish conditions under which higher dependence increases risk exposure and reduces profitability, using supermodular ordering techniques. Numerical results using a Clayton–Lévy copula demonstrate how dependence intensity and risk aversion impact optimal pricing strategies.