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M. Ngo, T. Nguyen and T. Duong

Abstract

We present counterparty risk by a jump in the underlying price and a structural change of the price process after the default of the counterparty. The default time is modeled by a default-density approach. Then we study an exponential utility-indifference price of an European option whose underlying asset is exposed to this counterparty risk. Utility-indifference pricing method normally consists in solving two optimization problems. However, by using the minimal entropy martingale measure, we reduce to solving just one optimal control problem. In addition, to overcome the incompleteness obstacle generated by the possible jump and the change in structure of the price process, we employ the BSDE-decomposition approach in order to decompose the problem into a global-before-default optimal control problem and an after-default one. Each problem works in its own complete framework. We demonstrate the result by numerical simulation of an European option price under the impact of jump’s size, intensity of the default, absolute risk aversion and change in the underlying volatility.

Open access

Duong Tan Nhut, Phan Le Ha Nguyen, Nguyen Trinh Don, N.T.T. Hien, Nguyen Phuc Huy, Nguyen Ba Nam, Bui The Vinh and Tran Cong Luan

Abstract

To achieve a better understanding of accumulation of paclitaxel and related taxanes in Himalayan yew (Taxus wallichiana Zucc.) callus mass, induction and growth of calli from needles and petioles under light-emitting diodes (LEDs) and production of paclitaxel and baccatin were investigated. Calli were induced from needles and petioles on Gamborg's B5 medium supplemented with 1 mg·l-1 kinetin and 4 mg·l-1 2,4-D under different com-binations of blue and red LEDs. Calli were further cultured in that medium under the same lighting conditions. Callus induction from needles and petioles and growth was better under blue LEDs than under red LEDs and fluorescent light. The combinations of blue and red LEDs produced variable results. The paclitaxel content of these calli was quantified by high-performance liquid chromatography. The paclitaxel content of calli derived from needles was 0.00628% and the 10-DAB (10-Deacetylbaccatin III) content was 0.00366%. The paclitaxel content of calli derived from petioles was 0.00412%, and no 10-DAB was detected.