Actuarial Pricing with Financial Methods

The objective of this paper is twofold. On the one hand, the optimal combination of reinsurance and financial investment is studied under a general framework, since there is no specific type of reinsurance contract, there is no specific dynamics of the financial instruments, the financial market does not have to be free of frictions and there are no constraints with respect to the financial securities to be selected, that is, derivative assets may be involved too. On the other hand, it is pointed out how the optimal combination above may provide us with new premium principles making the global insurer risk vanish, this risk being computed with a co- coherent risk measure. The new premium principles seem to respect several properties which are desirable from both the analytical and the economic perspectives. Indeed, from an analytical viewpoint, they are continuous, homogeneous, and increasing, while from the economic viewpoint the premium principles lead to cheaper prices with respect to both the insurance market and the financial market. In other words, the premium principles make the insurer more competitive though the insurer's global risk is vanishing. General necessary and sufficient optimality conditions will be given, as well as closed forms for the solutions under appropriate assumptions. Special attention will deserve those methods preventing unbounded optimization problems and a particular case will be more thoroughly studied, namely, the combination of the Black-Scholes- Merton pricing model with the conditional value at risk.