8,644 research outputs found
B-spline techniques for volatility modeling
This paper is devoted to the application of B-splines to volatility modeling,
specifically the calibration of the leverage function in stochastic local
volatility models and the parameterization of an arbitrage-free implied
volatility surface calibrated to sparse option data. We use an extension of
classical B-splines obtained by including basis functions with infinite
support. We first come back to the application of shape-constrained B-splines
to the estimation of conditional expectations, not merely from a scatter plot
but also from the given marginal distributions. An application is the Monte
Carlo calibration of stochastic local volatility models by Markov projection.
Then we present a new technique for the calibration of an implied volatility
surface to sparse option data. We use a B-spline parameterization of the
Radon-Nikodym derivative of the underlying's risk-neutral probability density
with respect to a roughly calibrated base model. We show that this method
provides smooth arbitrage-free implied volatility surfaces. Finally, we sketch
a Galerkin method with B-spline finite elements to the solution of the partial
differential equation satisfied by the Radon-Nikodym derivative.Comment: 25 page
Parametric arbitrage-free models for implied smile dynamics
Based on the theory of Tangent Levy model [1] developed by R. Carmona and S. Nadtochiy, this thesis gives a paramatrized realization of dynamic implied smile.\ud
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After specifying a Dirac style Levy measure, we give argument about the consistency issue of our model with the Tangent Levy Model. A corresponding no arbitrage drift condition is derived for the parameters. Numerical setup under our model for option pricing and parameter estimation for calibration is given. Implementation results are illustrated in detail and in the end we provide with simulation results of one day ahead implied smile
Setting the optimal limit value of motor insurance coverage by stochastic optimization
In this paper, we provide an alternative to a passive approach to the selection of insurance products or policy con-ditions. Specifically, we propose a method to make a decision about the optimal limit value for motor insurance coverage. Respecting the stochastic nature of individual loss, we formulate a problem of stochastic programming in which the total potential financial loss of the policyholder is minimized. Actually, we present a general optimization problem in which various relevant probability distributions of individual loss may be considered. In addition, we extend the work of Valecký (2017) and derive an insurance rate that describes better the dependence between the pure premium and the given limit value under the assumption that the individual potential loss follows a gamma distribution. Because of the absence of a closed-form solution, sample average approximation is applied to the objective function and the optimal solution to this approximated (SAA) problem is determined. Finally, the quality of the obtained solution is assessed by approximation to the optimality gap representing the difference between our candidate and the true solution
Multi-objective optimization for the geometry of trapezoidal corrugated morphing skins
Morphing concepts have great importance for the design of future aircraft as they provide the opportunity for the aircraft to adapt their shape in flight so as to always match the optimal configuration. This enables the aircraft to have a better performance, such as reducing fuel consumption, toxic emissions and noise pollution or increasing the maneuverability of the aircraft. However the requirements of morphing aircraft are conflicting from the structural perspective. For instance the design of a morphing skin is a key issue since it must be stiff to withstand the aerodynamic loads, but flexible to enable the large shape changes. Corrugated sheets have remarkable anisotropic characteristics. As a candidate skin for a morphing wing, they are stiff to withstand the aerodynamic loads and flexible to enable the morphing deformations. This work presents novel insights into the multi-objective optimization of a trapezoidal corrugated core with elastomer coating. The geometric parameters of the coated composite corrugated panels are optimized to minimize the in-plane stiffness and the weight of the skin and to maximize the flexural out-of-plane stiffness of the skin. These objective functions were calculated by use of an equivalent finite element code. The gradient-based aggregate method is selected to solve the optimization problem and is validated by comparing to the GA multi-objective optimization technique. The trend of the optimized objectives and parameters are discussed in detail; for example the optimum corrugation often has the maximum corrugation height. The obtained results provide important insights into the design of morphing corrugated skins
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Modeling of novel resist technologies
In response to the difficulties posed by the resolution, line edge roughness, sensitivity (RLS) trade-off to traditional chemically amplified resist (CAR) systems used for extreme ultraviolet lithography, a number of novel resist technologies have been proposed. In this paper, the effect of quencher loading on three resist technologies is analyzed via an error propagation-based resist simulator. In order of increasing novelty as well as complexity, they are: Conventional CAR with quencher, CAR with photodecomposable base, and PSCAR 2.0, a CAR system with photodecomposable base as well as an EUV-activated UV-sensitive resist component. Simulation finds the more complicated resist systems trade in an increase in resist stochastics for improved deprotection slopes, yielding a net benefit in terms of line width roughness
Demand uncertainty In modelling WDS: scaling laws and scenario generation
Water distribution systems (WDS) are critical infrastructures that should be designed to work properly in different conditions. The design and management of WDS should take into account the uncertain nature of some system parameters affecting the overall reliability of these infrastructures. In this context, water demand represents the major source of uncertainty. Thus, uncertain demand should be either modelled as a stochastic process or characterized using statistical tools. In this paper, we extend to the 3rd and 4th order moments the analytical equations (namely scaling laws) expressing the dependency of the statistical moments of demand signals on the sampling time resolution and on the number of served users. Also, we describe how the probability density function (pdf) of the demand signal changes with both the increase of the user’s number and the sampling rate variation. With this aim, synthetic data and real indoor water demand data are used. The scaling laws of the water demand statistics are a powerful tool which allows us to incorporate the demand uncertainty in the optimization models for a sustainable management of WDS. Specifically, in the stochastic/robust optimization, solutions close to the optimum in different working conditions should be considered. Obviously, the results of these optimization models are strongly dependent on the conditions that are taken into consideration (i.e. the scenarios). Among the approaches for the definition of demand scenarios and their probability-weight of occurrence, the moment-matching method is based on matching a set of statistical properties, e.g. moments from the 1st (mean) to the 4th (kurtosis) order
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