Prof. Yuliya Mishura: PhD course

Prof. Yuliya Mishura: PhD course

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Stochastic differential equations involving fractional Brownian motion

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fractional Brownian motion

stochastic differential equations

Lecture 6: Functional limit theorems for…

duration 1 hour 52 minutes

Lecture 6: Functional limit theorems for…

Lecture 6: Functional limit theorems for financial markets with long-range dependence

From Tiziano Vargiolu

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* General conditions of weak convergence - Convergence of sums - Multiplicative scheme* Monotonicity along the diagonal of a triangular matrix in the Cholesky…
$Thumbnail for entry Lecture 5: Fractional irregularity and fractional hedging$

Lecture 5: Fractional irregularity and fractional…

duration 1 hour 57 minutes

Lecture 5: Fractional irregularity and fractional…

Lecture 5: Fractional irregularity and fractional hedging

From Tiziano Vargiolu

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- Asymptotic behavior of maximal functionals - Representation results for Gaussian processes that create the generalized quasi-helix - Representation theorems for Holder…
Lecture 4: Application of Malliavin calculus to…

duration 1 hour 53 minutes

Lecture 4: Application of Malliavin calculus to…

Lecture 4: Application of Malliavin calculus to exact and approximate option pricing under stochastic volatility

From Tiziano Vargiolu

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Introduction Model of asset price and payoff function: additional assumptions, auxiliary properties Elements of Malliavin calculus and application to option pricing The…
Lecture 3: “Sandwiched” equations

duration 1 hour 42 minutes

Lecture 3: “Sandwiched” equations

Lecture 3: “Sandwiched” equations

From Tiziano Vargiolu

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What drifts allow to consider low values of H in SDE.
Lecture 2: Equations with unbounded coefficients…

duration 1 hour 41 minutes

Lecture 2: Equations with unbounded coefficients…

Lecture 2: Equations with unbounded coefficients and H > 1/2

From Tiziano Vargiolu

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1. Cox-Ingersoll-Ross equations with fBm. 2. Equations with unbounded drift. 3. Reflected Ornstein-Uhlenbeck equations.
Lecture 1: Standard stochastic differential…

duration 1 hour 49 minutes

Lecture 1: Standard stochastic differential…

Lecture 1: Standard stochastic differential equations with fBm

From Tiziano Vargiolu

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1. Integration with respect to fBm. 2. Elements of fractional and fractional stochastic calculus. 3. Stochastic differential equations with fBm and smooth coefficients.

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