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In this paper, we prove the global risk optimality of the hedging strategy ofcontingent claim, which is explicitly (or called semi-explicitly) constructedfor an incomplete financial market with external risk factors of non-GaussianOrnstein-Uhlenbeck (NGOU) processes. Analytical and numerical examples are bothpresented to illustrate the effectiveness of our optimal strategy. Our studyestablishes the connection between our financial system and existing generalsemimartingale based discussions by justifying required conditions. Moreprecisely, there are three steps involved. First, we firmly prove theno-arbitrage condition to be true for our financial market, which is used as anassumption in existing discussions. In doing so, we explicitly construct thesquare-integrable density process of the variance-optimal martingale measure(VOMM). Second, we derive a backward stochastic differential equation (BSDE)with jumps for the mean-value process of a given contingent claim. The uniqueexistence of adapted strong solution to the BSDE is proved under suitableterminal conditions including both European call and put options as specialcases. Third, by combining the solution of the BSDE and the VOMM, we reach thejustification of the global risk optimality for our hedging strategy.

Mean-variance hedging based on an incomplete market with external risk factors of non-Gaussian OU processes