Biagini, Francesca; Guasoni, Paolo Mean-variance hedging with random volatility jumps. (English) Zbl 1035.91028 Stochastic Anal. Appl. 20, No. 3, 471-494 (2002). From authors’ abstract: The authors introduce a general framework for stochastic volatility models, with the risk asset dynamics given by: \[ dX_t(\omega,\eta)= \mu_t(\eta) X_t(\omega, \eta)\,dt+ \sigma_t(\eta) X_t(\omega, \eta)\,dW_t(\omega), \] where \((\omega,\eta)\in (\Omega\times H, {\mathcal T}^\Omega\otimes{\mathcal T}^H, P^\Omega\otimes P^H)\). In particular, the authors allow for random discontinuities in the volatility \(\sigma\) and the drift \(\mu\). First it is characterized the set of equivalent martingale measures, then compute the mean-variance optimal measure \(\widetilde P\), using some results of Schweizer on the existence of an adjustment process \(\beta\). It is shown the examples where the risk premium \(\lambda= (\mu-r)/\sigma\) follows a discontinuous process, and explicit calculations for \(\widetilde P\). Reviewer: C. L. Parihar (Indore) Cited in 4 Documents MSC: 91B28 Finance etc. (MSC2000) 60H30 Applications of stochastic analysis (to PDEs, etc.) Keywords:stochastic volatility models; mean-variance optimal measure; change of numéraire PDF BibTeX XML Cite \textit{F. Biagini} and \textit{P. Guasoni}, Stochastic Anal. Appl. 20, No. 3, 471--494 (2002; Zbl 1035.91028) Full Text: DOI OpenURL