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Showing 1 to 9 of 9 for “"Levy process"”.
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Malliavin Calculus in the Canonical Levy Process: White Noise Theory and Financial Applications.
… a white noise theory for the Canonical Levy process by Sole, Utzet, and Vives. The construction is based on the alternative construction of the chaos expansion of square integrable random variable. Then, we showed a Clark-Ocone theorem in L^2(P) and under the change of measure. The …
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Optimal inspection and maintenance for stochastically deteriorating systems
… may be modelled by a continuous time stochastic process. Our emphasis is mainly on using the information gained from inspecting the degradation to determine efficient maintenance and inspection policies. The system we shall consider is one in which the degradation is modelled by a Levy process, …
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Free products of operator spaces and free Markov processes
… of the two C*-algebras.</p><p>Free Markov processes are also investigated in Voiculescu's free probability theory. This highly non-commutative notion generalizes that of free Brownian motion and free Levy processes. Some free Markov processes are realized as solutions to free stochastic …
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Analytical Methods For Levy Processes With Applications To Finance
… a self-contained introduction to some popular Levy models and to two key objects from the theory of Levy processes: the Wiener-Hopf factors and the exponential functional. We pay special attention to techniques and results associated with two “analytically tractable” families of processes known …
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Stochastic Volatility with Levy Processes: Calibration and Pricing
In this thesis, stochastic volatility models with Levy processes are treated in parameter calibration by the Carr-Madan fast Fourier transform (FFT) method and pricing through the partial integro-differential equation (PIDE) approach. First, different models where the underlying log stock price or …
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Sampling error of the supremum of a Lévy process
… supremum and discrete maximum of a Lévy process that is often used in finance. We will show that the expected difference is a quantity that highly depends on the variational property of the underlying Lévy process. Two techniques are used with respect to the cases of the complexity of the …
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Non-Gaussian Stochastic Process Priors for Learning
… such as finance, climate science, and signal processing, where extreme events and rare fluctuations play critical roles. A suitable generalisation of the well-known Brownian motion, which is a foundational tool in Gaussian modelling, is the family of L\'evy processes that display varying …
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Some Insurance Options on Stochastic Drawdowns
Insurance and options have been often used by investors to protect themselves from market crashes and significant financial losses. Thanks to its desired features, drawdowns can be a very useful tool in the marketplace, allowing investors to protect against the downside risks which commonly occur …
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Lévy Processes in Finance: Theory, Numerics, and Empirical Facts
Levy-Prozesse, das heißt stochastische Prozesse mit unabhängigen <br>und stationären Zuwächsen, stellen eine Verallgemeinerung der <br>Brownschen Bewegung dar. Aufgrund ihrer günstigen analytischen <br>Eigenschaften hat sich die Brownsche Bewegung als Standardmodell <br>für viele Prozesse in der …