Resumen de Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets

Yimin Kao, Liping Xu, Hani Jamal Sulaimani

• The pricing and hedging of financial derivatives have become one of the hot research issues in mathematical finance today.In the case of non-risk neutrality, this article uses the martingale method and probability measurement method to studythe pricing method and hedging strategy of financial derivatives. This paper also further studies the hedging strategyof financial derivatives in the incomplete market based on the BSM model and converts the solution of this problem intosolving a vector on the Hilbert space to its closure. The problem of space projection is to use projection theory to decomposefinancial derivatives under a given martingale measure. In the imperfect market, the vertical projection theory is used toobtain the approximate pricing method and hedging strategy of financial derivatives in which the underlying asset followsthe martingale process; the projection theory is further expanded, and the pricing problem of financial derivatives under themixed-asset portfolio is obtained. Approximate pricing of financial derivatives; in the discrete state, the hedging investmentstrategy of financial derivatives H in the imperfect market is found through the method of variance approximation.