Actuarial approach to option pricing in a fractional Black-Scholes model with time-dependent volatility (Q2866791)

The paper concerns a continuous-time market model with the asset price driven by the stochastic equation NEWLINE\[NEWLINE S_t=S_0+\int_0^t\mu(u)S_u\mathrm du +\int_0^t\sigma(u)S_u\mathrm d B_u^H,\qquad t\in[0, T], NEWLINE\]NEWLINE where \(\mu,\; \sigma\) are some deterministic \(C^1[0, T]\) functions and \(B^H\) is a fractional Brownian motion.NEWLINENEWLINEThe author proves the existence and uniqueness of the average risk-neutral measure \(Q\) and considers the fair price of the European options.NEWLINENEWLINEThe fractional Black-Scholes formula is presented.