An investor faced with a contingent claim may eliminate risk by perfect hedging, but as it is often quite expensive, he seeks partial hedging (quantile hedging or efficient hedging) that requires less capital and reduces the risk. Efficient hedging for European call option was considered in the standard Black-Scholes model with constant drift and volatility coefficients. In this paper we considered the efficient hedging for European call option in general Black-Scholes model dX_t=X_t(m(t)dt+\sigma (t)dw(t)) with time-varying drift and volatility coefficients and in fractional Black-Scholes model dX_t=X_t( mdt+\sigma dB _H(t)  ) with constant coefficients.
An investor faced with a contingent claim may eliminate risk by perfect hedging, but as it is often quite expensive, he seeks partial hedging (quantile hedging or efficient hedging) that requires less capital and reduces the risk. Efficient hedging for European call option was considered in the standard Black-Scholes model with constant drift and volatility coefficients. In this paper we considered the efficient hedging for European call option in general Black-Scholes model dX_t=X_t(m(t)dt+\sigma (t)dw(t)) with time-varying drift and volatility coefficients and in fractional Black-Scholes model dX_t=X_t( \sigma B _H(t) +mdt ) with constant coefficients.
R
mdt+\sigma dB
\sigma B
A
+mdt