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We examine in this article the pricing of target volatility options in the lognormal fractional SABR model. A decomposition formula by Itô's calculus yields a theoretical replicating strategy for the target volatility option, assuming the accessibilities of all variance swaps and swaptions. The same formula also suggests an approximation formula for the price of target volatility option in small time by the technique of freezing the coefficient. Alternatively, we also derive closed formed expressions for a small volatility of volatility expansion of the price of target volatility option. Numerical experiments show accuracy of the approximations in a reasonably wide range of parameters.

This paper considers the suboptimal H∞ control problem for linear discrete-time algebraic dynamical systems. Such systems can be formally described as LTI (linear and timeinvariant) discrete-time systems, whose transfer function matrix is allowed to be improper or polynomial. The parametrization of output feedback controllers is given in a realization-based setting involving two generalized algebraic Riccati equations and features the same elegant simplicity of the standard (proper) case. Two relevant numerical examples prove the effectiveness of our approach.

For an uncertain differential-algebraic system subject to perturbations acting additively on coprime factors of its transfer function matrix, we construct a robust stabilizing controller and give a formula for the maximum stability margin in terms of realizations and solutions to appropriate Riccati equations.

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