| The classic ?-hedging strategy is derived from the It? formula and some theories of partial differential equations.However,when dealing with some complex pathdependent options(such as lookback options),the unsmooth nature of the payoff function of such options will lead to expensive numerical estimation costs at the same time,because of the uncertainty in the financial market,it is inaccurate to describe the pricing and hedging of options only from the perspective of randomness.To solve these problems,this paper studies a method of using Malliavin calculus to hedge the lookback option with fixed strike price in fuzzy space,the details are as follows:Firstly,the Clark-Ocone formula in fuzzy space is proved by combining the relevant definitions and properties of fuzzy stochastic integral and Malliavin calculus.Secondly,the fuzzy stochastic differential equation based on the Skorohod meaning is used as the pricing model for lookback options,and the unique solution of the equation is obtained and treated as a fuzzy set.Combining the self financing portfolio strategy of lookback options,the expression of hedging portfolio can be obtained by applying the fuzzy Clark-Ocone formula to the price process of the portfolio.Finally,according to the reflection principle,Esscher transformand and other techniques,the analytical formula of the hedge portfolio is calculated as a fuzzy interval.In the part of numerical experiment,by showing the sensitivity of the portfolio to the model parameters,it is concluded that the biggest factor affecting the portfolio is volatility,and according to the subjective judgment of financial investors,the permissible range of the expected hedge portfolio is given. |
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