  In this paper, we prove the global risk optimality of the hedging strategy of
contingent claim, which is explicitly (or called semi-explicitly) constructed
for an incomplete financial market with external risk factors of non-Gaussian
Ornstein-Uhlenbeck (NGOU) processes. Analytical and numerical examples are both
presented to illustrate the effectiveness of our optimal strategy. Our study
establishes the connection between our financial system and existing general
semimartingale based discussions by justifying required conditions. More
precisely, there are three steps involved. First, we firmly prove the
no-arbitrage condition to be true for our financial market, which is used as an
assumption in existing discussions. In doing so, we explicitly construct the
square-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 unique
existence of adapted strong solution to the BSDE is proved under suitable
terminal conditions including both European call and put options as special
cases. Third, by combining the solution of the BSDE and the VOMM, we reach the
justification of the global risk optimality for our hedging strategy.
