In this article, we show, in the context of partial hedging, that some important relationships about comonotonicity and convex order cannot be translated to counter-monotonicity in general because of the possibility of over-hedging. We propose a new notion called proper hedge that can e...

A general class of fair valuations which are both market-consistent (mark-to-market for any hedgeable part of a claim) and actuarial (mark-to-model for any claim that is independent of financial market evolutions) was introduced in Dhaene et al. in a single period framework. In particular, the...

Hedging techniques have been widely adopted in market-consistent or fair valuation approach required by recent solvency regulations, to take into account the market prices of the hedgeable parts of insurance liabilities. In this study, we investigate the fair dynamic valuation of insurance...