On the (in-)dependence between financial and actuarial risks

Probability statements about future evolutions of financial and actuarial risks are expressed in terms of the ‘real-world’ probability measure P, whereas in an arbitrage-free environment, the prices of these traded risks can be expressed in terms of an equivalent martingale measure Q. The assumption of independence between financial and actuarial risks in the real world may be quite reasonable in many situations. Making such an independence assumption in the pricing world however, may be convenient but hard to understand from an intuitive point of view. In this pedagogical paper, we investigate the conditions under which it is possible (or not) to transfer the independence assumption from P to Q. In particular, we show that an independence relation that is observed in the P-world can often not be maintained in the Q-world.