We study the problem of parameter estimation for stochastic differential equations with small noise and fast oscillating parameters. Depending on how fast the intensity of the noise goes to zero relative to the homogenization parameter, we consider three different regimes. For each regime, we...

Based on Malliavin calculus tools and approximation results, we show how to compute a maximum likelihood type estimator for a rather general differential equation driven by a fractional Brownian motion with Hurst parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$H1/2$$</EquationSource> </InlineEquation>. Rates of convergence for the approximation task are provided,...</equationsource></inlineequation>

It is commonly accepted that certain financial data exhibit long-range dependence. We consider a continuous-time stochastic volatility model in which the stock price is Geometric Brownian Motion with volatility described by a fractional Ornstein--Uhlenbeck process. We also study two...

We investigate optimal portfolio selection problems with mispricing and model ambiguity under a financial market which contains a pair of mispriced stocks. We assume that the dynamics of the pair satisfies a “cointegrated system” advanced by Liu and Timmermann in a 2013 manuscript. The...

The problem of option pricing is treated using the Stochastic Volatility (SV) model: the volatility of the underlying asset is a function of an exogenous stochastic process, typically assumed to be mean-reverting. Assuming that only discrete past stock information is available, an interacting...