Weekly Bulletin

How should an insurer price a new contract when it wants to account for the dependence between the new risk and its existing portfolio? This talk introduces a new premium principle—the conditional indifference premium—which explicitly incorporates the insurer’s current portfolio as background risk. Unlike classical law-invariant pricing rules, this approach captures the dependence between the new risk and existing exposures, yielding prices that better reflect diversification and accumulation effects. The talk will present the theoretical foundations of the conditional indifference premium, explore its axiomatic and stochastic dominance properties, and highlight its connection to risk measures and regulatory capital. Through examples with exchangeable portfolios, we illustrate how portfolio size and dependence structure influence the marginal price of additional risks, shedding new light on the limits of diversification in insurance pricing.