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Since 1973 classic Black-scholes option pricing theory since the advent of option pricing and hedging strategies have become a financial study of the core issues. Black-scholes option pricing theory is based on a discussion of the following arbitrage: Continuous adjustment of a risk-free bonds include stocks and portfolio positions, investors can just copy any work based on the stock option income, and the value of the option will be equal to the cost of reproduction. Black-scholes theory is that in the absence of market frictions obtained under the conditions, if there is transaction costs discussed above is no longer valid, no matter how small transaction costs, continuous position adjustment will bring huge transaction costs. Leland (1985) considered the case with transaction costs replication options put forward a modified transaction costs depend on the size and the option to adjust the frequency of replication strategy, and when the transaction cost becomes arbitrarily hours this strategy tends to Black-scholes strategy . However, Leland adjust the position of the time limit copying at equal time intervals. We make the time interval can be a hedge against changes in the amount of time each hedge consists of a smooth, positive, strictly increasing function gives a single, satisfy: f (t i ) = iδ different function f (t) represents hedge time t i different distributions. In particular, if we can obtain f (t) = t when Leland is considered a model, we also assume that the stock price X t satisfies the following stochastic differential equation: dx t / x t = μdt σdB t where B t is a standard Brownian motion, μ is the stock price drift rate, σ is volatility. Definition t i time value of the stock held by: s (t i , X t i ) = x t i C x (t i , X t i < / sub>) Hope is chlorine paragraph where the function c (t, x) specifies the maturity T t get a random income: time portfolio composition, in accordance with the function c (t, x) hedge in the ..., eight. s (t,, xr),,. , S (t '1, x,: ) s (t:, Ge). With [X, j = C sigh U, Xn Xi) - Yan X' an X) a D, l - one-IX ',, z, u households Yin Yue Z, return to the mountain a spoon z Meng / ...' a d timber x, 'a timber Ge; Ge right of the first one is the initial wealth, and the second term represents the ti ti, between the number of shares held by the product with the stock price changes, the third term is the rebalancing transaction costs, the transaction costs expressed as Wu. When a hedging interval ti, a t 'and transaction costs are at a rate tends to o, we obtain a complete hedging strategy, that is, Theorem 1. Theorem 1, assuming revenue function u (x) has strictly positive second-order derivative, f (t) 20 strictly increasing and the interval fo, month has a continuous second derivative, defined, (t) three of the; surface, so that death (t, b) the following equation: 1, << / sub> sub> 2 Hall, . · c, two J \, 0 and p = dZ, are: \approximated discrete hedging error of this approximation is expressed by the following theorem: Theorem 2: Under the conditions of Theorem 1 :: (v) an E {(u Counseling (X :) a u (X :)), }
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