Titlebook: Seminar on Stochastic Analysis, Random Fields and Applications III; Centro Stefano Frans Robert C. Dalang,Marco Dozzi,Francesco Russo Confe

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On the Superreplication Approach for European Interest Rates Derivatives,neral results of [.] and [.] to prove that the minimal superstrategy is given by the solution of a nonlinear PDE associated to the model, that is the so-called Black-Scholes-Barenblatt (BSB) equation. In particular we show how this approach applies to the case of caps and floors extending results of

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A Complete Market Model with Poisson and Brownian Components,g each other. The chaotic calculus relative to this martingale is developed, and applications to the computation of hedging strategies are presented via a Clark formula and the method of partial differential equations.

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A Bayesian Adaptive Control Approach to Risk Management in a Binomial Model,the general discrete time model and the approach described in Runggaldier and Zaccaria (1999), we derive explicit analytic solutions for the particular case of a binomial model when there is uncertainty about the probability of an “up-movement”. The solution turns out to be a rather intuitive extens

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Regularity Conditions for Parabolic SPDEs on Lie Groups,ltrami operator on ., and where . is a Gaussian space-correlated noise, which is white-noise in time. We find necessary and sufficient conditions on the space correlation of . such that . exists or is a Hölder-continuous function in the spatial variable ., using some basic tools of stochastic analys

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Instability of a Quantum Particle Induced by a Randomly Varying Spring Coefficient,in terms of a jump process. Using standard probability tools, we are then able to compute explicitly the probabilities for observing the different energy eigenstates and give the exact statistical distribution of the energy of the particle.

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Light, Atoms, and Singularities, time goes to infinity is studied, in particular drawing on methods from renewal theory. Results from this type of study have been instrumental for the understanding and improvement of the efficiency of the cooling schemes.

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