733 research outputs found
Approximations of Stochastic Partial Differential Equations
In this paper we show that solutions of stochastic partial differential
equations driven by Brownian motion can be approximated by stochastic partial
differential equations forced by pure jump noise/random kicks. Applications to
stochastic Burgers equations are discussed
A Malliavin-Skorohod calculus in and for additive and Volterra-type processes
In this paper we develop a Malliavin-Skorohod type calculus for additive
processes in the and settings, extending the probabilistic
interpretation of the Malliavin-Skorohod operators to this context. We prove
calculus rules and obtain a generalization of the Clark-Hausmann-Ocone formula
for random variables in . Our theory is then applied to extend the
stochastic integration with respect to volatility modulated L\'evy-driven
Volterra processes recently introduced in the literature. Our work yields to
substantially weaker conditions that permit to cover integration with respect,
e.g. to Volterra processes driven by -stable processes with . The presentation focuses on jump type processes.Comment: 27 page
Robustness of quadratic hedging strategies in finance via backward stochastic differential equations with jumps
We consider a backward stochastic differential equation with jumps (BSDEJ)
which is driven by a Brownian motion and a Poisson random measure. We present
two candidate-approximations to this BSDEJ and we prove that the solution of
each candidate- approximation converges to the solution of the original BSDEJ
in a space which we specify. We use this result to investigate in further
detail the consequences of the choice of the model to (partial) hedging in
incomplete markets in finance. As an application, we consider models in which
the small variations in the price dynamics are modeled with a Poisson random
measure with infinite activity and models in which these small variations are
modeled with a Brownian motion. Using the convergence results on BSDEJs, we
show that quadratic hedging strategies are robust towards the choice of the
model and we derive an estimation of the model risk
Stime di Smoothing-Strichartz per NLS ed applicazioni
In questa tesi abbiamo voluto ottenere delle stime di tipo Strichartz per NLS con potenziale elettrostatico non passando per i classici metodi dell'analisi funzionale generalmente usati nel caso di laplaciano libero.
Prendendo spunto da lavori di Burq e Kato abbiamo ricavato tali stime nel caso n maggiore o uguale a 3.
Inoltre, a livello applicato, attraverso delle simulazioni numeriche si è voluto esplicitare il fatto che sotto certe condizioni tali stime a priori risultano ingannevoli e quindi false
On the approximation of L\'evy driven Volterra processes and their integrals
Volterra processes appear in several applications ranging from turbulence to
energy finance where they are used in the modelling of e.g. temperatures and
wind and the related financial derivatives. Volterra processes are in general
non-semimartingales and a theory of integration with respect to such processes
is in fact not standard. In this work we suggest to construct an approximating
sequence of L\'evy driven Volterra processes, by perturbation of the kernel
function. In this way, one can obtain an approximating sequence of
semimartingales.
Then we consider fractional integration with respect to Volterra processes as
integrators and we study the corresponding approximations of the fractional
integrals. We illustrate the approach presenting the specific study of the
Gamma-Volterra processes. Examples and illustrations via simulation are given.Comment: 39 pages, 3 figure
Sensitivity analysis in a market with memory
A general market model with memory is considered in terms of stochastic
functional differential equations. We aim at representation formulae for the
sensitivity analysis of the dependence of option prices on the memory. This
implies a generalization of the concept of delta.Comment: Withdrawn by the authors due to an error in equation (2.6). A new
work is in preparatio
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