Long-Time Trajectorial Large Deviations and Importance Sampling for Affine Stochastic Volatility Models

We establish a pathwise large deviation principle for affine stochastic volatility models introduced by Keller-Ressel (2011), and present an application to variance reduction for Monte Carlo computation of prices of path-dependent options in these models, extending the method developed by Genin and Tankov (2020) for exponential Lévy models. To this end, we apply an exponentially affine change of measure and use Varadhan’s lemma, in the fashion of Guasoni and Robertson (2008) and Robertson (2010), to approximate the problem of finding the measure that minimizes the variance of the Monte Carlo estimator. We test the method on the Heston model with and without jumps to demonstrate its numerical efficiency.

Nuclear Data Uncertainty Propagation in Complex Fusion Geometries

The ASUSD program package was designed to automate and simplify the process of deterministic nuclear data sensitivity and uncertainty quantification. The program package couples Denovo, a discrete ordinate 3D transport solver, as part of ADVANTG and SUSD3D, a deterministic first order perturbation theory based Sensitivity/Uncertainty code, using several auxiliary programs used for input data preparation and post processing. Because of the automation employed in ASUSD, it is useful for Sensitivity/Uncertainty analysis of complex fusion geometries. In this paper, ASUSD was used to quantify uncertainties in the JET KN2 irradiation position. The results were compared to previously obtained probabilistic-based uncertainties determined using TALYS-based random nuclear data samples and MCNP in a Total Monte Carlo computation scheme. Results of the two approaches, deterministic and probabilistic, to nuclear data uncertainty propagation are compared and discussed. ASUSD was also used to perform preliminary Sensitivity/Uncertainty (S/U) analyses of three JET3-NEXP streaming benchmark experimental positions (A1, A4 and A7).

Nonparametric Malliavin–Monte Carlo Computation of Hedging Greeks

We propose a way to compute the hedging Delta using the Malliavin weight method. Our approach, which we name the λ-method, generally outperforms the standard Monte Carlo finite difference method, especially for discontinuous payoffs. Furthermore, our approach is nonparametric, as we only assume a general local volatility model and we substitute the volatility and the other processes involved in the Greek formula with quantities that can be nonparametrically estimated from a given time series of observed prices.

Computation of fission product deposition in aerosols

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] High-temperature gas-cooled reactors (HTGRs) generate carbonaceous dust during both normal operations and accidents. The dust particles can be both highly irregular and porous and have exceptionally large surface areas, making dust-facilitated fission product (FP) transport a major factor in the computation of the nuclear source term. Since the FP interactions with the dust can occur while the dust is on a surface as well as in suspension, there is a need to obtain computational and experimental results for both situations. Since the particle sizes of interest span a wide range, from nanometers to microns, and are porous with various pathways for FP interactions to occur, these computations need to include not only the continuum regime, but the transport regime as well where the particle (or pore) size is comparable to the vapor (FP) mean free path. The focus of this dissertation is on Monte Carlo computation of the condensation rate on chainlike particles and particle agglomerates in the transport regime, towards a better understanding of how aerosol geometry affects mass transport on those particles.