Huyên Pham

Mean-Variance Hedging and Numéraire

We consider the mean-variance hedging problem when the risky assets price process is a continuous semimartingale. The usual approach deals with self-financed portfolios with respect to the primitive assets family. By adding a numeraire as an asset to trade in, we show how self-financed portfolios may be expressed with respect to this extended assets family, without changing the set of attainable contingent claims. Copyright Blackwell Publishers Inc 1998.

Mean-variance hedging for continuous processes: New proofs and examples

Abstract. Let

The fundamental theorem of asset pricing with cone constraints

X

Local Risk-Minimization Under Transaction Costs

be a special semimartingale of the form

Sublinear price functionals under portfolio constraints

X=X_0+M+\int d\langle M\rangle\,\widehat\lambda

Large deviation probabilities in estimation of Poisson random measures

and denote by

Large deviations in estimation of an Ornstein-Uhlenbeck model

\widehat K=\int \widehat\lambda^{\rm tr}\,d\langle M\rangle\,\widehat\lambda

Large deviation principle in nonparametric estimation of marked point processes

the mean-variance tradeoff process of

Super-replication in stochastic volatility models under portfolio constraints

X

Hedging in discrete time under transaction costs and continuous-time limit

. Let