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Stochastic differential equations with constraints driven by processes with bounded p-variation

Falkowski A., Słomiński L.

Probability and Mathematical Statistics

2015

Vol. 35, Fasc. 2

343--365

We study the existence, uniqueness and approximation of solutions of stochastic differential equations with constraints driven by processes with bounded p-variation. Our main tool are new estimates showing Lipschitz continuity of the deterministic Skorokhod problem in p-variation norm. Applications to fractional SDEs with constraints are given.

Actuarial Approach to Option Pricing in a Fractional Black–Scholes Model with Time-Dependent Volatility

Falkowski A.

Bulletin of the Polish Academy of Sciences. Mathematics

2013

Vol. 61, no 2

181--193

We study actuarial methods of option pricing in a fractional Black–Scholes model with time-dependent volatility. We interpret the option as a potential loss and we show that the fair premium needed to insure this loss coincides with the expectation of the discounted claim payoff under the average risk neutral measure.