Search results for " 60G51"
showing 4 items of 4 documents
CALIBRATION OF LÉVY PROCESSES USING OPTIMAL CONTROL OF KOLMOGOROV EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS
2018
We present an optimal control approach to the problem of model calibration for L\'evy processes based on a non parametric estimation procedure. The calibration problem is of considerable interest in mathematical finance and beyond. Calibration of L\'evy processes is particularly challenging as the jump distribution is given by an arbitrary L\'evy measure, which form a infinite dimensional space. In this work, we follow an approach which is related to the maximum likelihood theory of sieves. The sampling of the L\'evy process is modelled as independent observations of the stochastic process at some terminal time $T$. We use a generic spline discretization of the L\'evy jump measure and selec…
Malliavin derivative of random functions and applications to L��vy driven BSDEs
2014
We consider measurable $F: ��\times \mathbb{R}^d \to \mathbb{R}$ where $F(\cdot, x)$ belongs for any $x$ to the Malliavin Sobolev space $\mathbb{D}_{1,2}$ (with respect to a L��vy process) and provide sufficient conditions on $F$ and $G_1,\ldots,G_d \in \mathbb{D}_{1,2}$ such that $F(\cdot, G_1,\ldots,G_d) \in \mathbb{D}_{1,2}.$ The above result is applied to show Malliavin differentiability of solutions to BSDEs (backward stochastic differential equations) driven by L��vy noise where the generator is given by a progressively measurable function $f(��,t,y,z).$
Futures pricing in electricity markets based on stable CARMA spot models
2012
We present a new model for the electricity spot price dynamics, which is able to capture seasonality, low-frequency dynamics and the extreme spikes in the market. Instead of the usual purely deterministic trend we introduce a non-stationary independent increments process for the low-frequency dynamics, and model the large uctuations by a non-Gaussian stable CARMA process. The model allows for analytic futures prices, and we apply these to model and estimate the whole market consistently. Besides standard parameter estimation, an estimation procedure is suggested, where we t the non-stationary trend using futures data with long time until delivery, and a robust L 1 -lter to nd the states of …
Invariant Markov semigroups on quantum homogeneous spaces
2019
Invariance properties of linear functionals and linear maps on algebras of functions on quantum homogeneous spaces are studied, in particular for the special case of expected coideal *-subalgebras. Several one-to-one correspondences between such invariant functionals are established. Adding a positivity condition, this yields one-to-one correspondences of invariant quantum Markov semigroups acting on expected coideal *-subalgebras and certain convolution semigroups of states on the underlying compact quantum group. This gives an approach to classifying invariant quantum Markov semigroups on these quantum homogeneous spaces. The generators of these semigroups are viewed as Laplace operators …