The paper discusses the problem of hedging not perfectly replicable contingent claims by using a benchmark, the numerraire portfolio, as reference unit. The proposed concept of benchmarked risk minimization generalizes classical risk minimization, pioneered by Follmer, Sondermann and Schweizer....

This paper considers a class of incomplete financial market models with security price processes that exhibit intensity based jumps. The benchmark or numeraire is chosen to be the growth optimal portfolio. Portfolio values, when expressed in units of the benchmark, are local martingales. In...

This paper describes a financial market modelling framework that exploits the notion of a deflator. The demonstrations of the deflator measured in units of primary assets form a minimal set of basic financial quantities that completely specify overall market dynamics. Risk premia of asset prices...

The solution to the problem of hedging contingent claims by local risk-minimisation has been considered in detail in Follmer and Sondermann (1986), Follmer and Schweizer (1991) and Schweizer (1991). However, given a stochastic process Xt and tau1 tau2, the strategy that is locally...

Starting from the European option valuation framework of Chauveau and Gatfaoui (2002), we establish the link with stochastic volatility models. And, we propose both a new vision and a general framework for valuing European options in the light of systematic and idiosyncratic risks affecting...