A Unified Model for XVA, including Interest Rates and Rating

We start in Chapter 2 to investigate linear matrix-valued SDEs and the Itô-stochastic Magnus expansion. The Itô-stochastic Magnus expansion provides an efficient numerical scheme to solve matrix-valued SDEs. We show convergence of the expansion up to a stopping time τ and provide an asymptotic estimate of the cumulative distribution function of τ. Moreover, we show how to apply it to solve SPDEs with one and two spatial dimensions by combining it with the method of lines with high accuracy. We will see that the Magnus expansion allows us to use GPU techniques leading to major performance improvements compared to a standard Euler-Maruyama scheme. In Chapter 3, we study a short-rate model in a Cox-Ingersoll-Ross (CIR) framework for negative interest rates. We define the short rate as the difference of two independent CIR processes and add a deterministic shift to guarantee a perfect fit to the market term structure. We show how to use the Gram-Charlier expansion to efficiently calibrate the model to the market swaption surface and price Bermudan swaptions with good accuracy. We are taking two different perspectives for rating transition modelling. In Section 4.4, we study inhomogeneous continuous-time Markov chains (ICTMC) as a candidate for a rating model with deterministic rating transitions. We extend this model by taking a Lie group perspective in Section 4.5, to allow for stochastic rating transitions. In both cases, we will compare the most popular choices for a change of measure technique and show how to efficiently calibrate both models to the available historical rating data and market default probabilities. At the very end, we apply the techniques shown in this thesis to minimize the collateral-inclusive Credit/ Debit Valuation Adjustments under the constraint of small collateral postings by using a collateral account dependent on rating trigger.

Response times in computerized adaptive testing: a method for cheating detection

In the field of educational and psychological measurement, the shift from paper-based to computerized tests has become a prominent trend in recent years. Computerized tests allow for more complex and personalized test administration procedures, like Computerized Adaptive Testing (CAT). CAT, following the Item Response Theory (IRT) models, dynamically generates tests based on test-taker responses, driven by complex statistical algorithms. Even if CAT structures are complex, they are flexible and convenient, but concerns about test security should be addressed. Frequent item administration can lead to item exposure and cheating, necessitating preventive and diagnostic measures. In this thesis a method called "CHeater identification using Interim Person fit Statistic" (CHIPS) is developed, designed to identify and limit cheaters in real-time during test administration. CHIPS utilizes response times (RTs) to calculate an Interim Person fit Statistic (IPS), allowing for on-the-fly intervention using a more secret item bank. Also, a slight modification is proposed to overcome situations with constant speed, called Modified-CHIPS (M-CHIPS). A simulation study assesses CHIPS, highlighting its effectiveness in identifying and controlling cheaters. However, it reveals limitations when cheaters possess all correct answers. The M-CHIPS overcame this limitation. Furthermore, the method has shown not to be influenced by the cheaters’ ability distribution or the level of correlation between ability and speed of test-takers. Finally, the method has demonstrated flexibility for the choice of significance level and the transition from fixed-length tests to variable-length ones. The thesis discusses potential applications, including the suitability of the method for multiple-choice tests, assumptions about RT distribution and level of item pre-knowledge. Also limitations are discussed to explore future developments such as different RT distributions, unusual honest respondent behaviors, and field testing in real-world scenarios. In summary, CHIPS and M-CHIPS offer real-time cheating detection in CAT, enhancing test security and ability estimation while not penalizing test respondents.

Loops, Chains, Sheets, and Networks from Variable Coordination of Cu(hfac)(2) with a Flexibly Hinged Aminoxyl Radical Ligand

One pair of reactants, Cu(hfac)(2) = M and the hinge-flexible radical ligand 5-(3-N-tert-butyl-N-aminoxylphenyl)pyrimidine (3PPN = L), yields a diverse set of five coordination complexes: a cyclic loop M(2)L(1) dimer; a 1:1 cocrystal between an M(2)L(2) loop and an ML(2) fragment; a ID chain of M(2)L(2) loops linked by M; two 2D M(3)L(2) networks of (M-L)(n) chains crosslinked by M with different repeat length pitches; a 3D M(3)L(2) network of M(2)L(2) loops cross-linking (M-L)(n)-type chains with connectivity different from those in the 2D networks. Most of the higher dimensional complexes exhibit reversible, temperature-dependent spin-state conversion of high-temperature paramagnetic states to lower magnetic moment states having antiferromagnetic exchange within Cu-ON bonds upon cooling, with accompanying bond contraction. The 3D complex also exhibited antiferromagnetic exchange between Cu(II) ions linked in chains through pyrimidine rings.

Economic design of (X)over-bar charts with variable parameters: the Markov chain approach

This paper presents an economic design of (X) over bar control charts with variable sample sizes, variable sampling intervals, and variable control limits. The sample size n, the sampling interval h, and the control limit coefficient k vary between minimum and maximum values, tightening or relaxing the control. The control is relaxed when an (X) over bar value falls close to the target and is tightened when an (X) over bar value falls far from the target. A cost model is constructed that involves the cost of false alarms, the cost of finding and eliminating the assignable cause, the cost associated with production in an out-of-control state, and the cost of sampling and testing. The assumption of an exponential distribution to describe the length of time the process remains in control allows the application of the Markov chain approach for developing the cost function. A comprehensive study is performed to examine the economic advantages of varying the (X) over bar chart parameters.

AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

Fractional order modelling of zero length column desorption response for adsorbents with variable particle sizes

This manuscript analyses the data generated by a Zero Length Column (ZLC) diffusion experimental set-up, for 1,3 Di-isopropyl benzene in a 100% alumina matrix with variable particle size. The time evolution of the phenomena resembles those of fractional order systems, namely those with a fast initial transient followed by long and slow tails. The experimental measurements are best fitted with the Harris model revealing a power law behavior.

Association between EcoRI fragment-length polymorphism of the immunoglobulin lambda variable 8 (IGLV8) gene family with rheumatoid arthritis and systemic lupus erythematosus

The human immunoglobulin lambda variable 8 (IGLV8) subgroup is a gene family containing three members, one of them included in a monomorphic 3.7-kb EcoRI genomic fragment located at the major lambda variable locus on chromosome 22q11.1 (gene IGLV8a, EMBL accession No. Z73650) at 100% frequency in the normal urban population. The second is a polymorphic RFLP allele included in a 6.0-kb EcoRI fragment at 10% frequency, and the third is located in a monomorphic 8.0-kb EcoRI fragment at 100% frequency, the last being translocated to chromosome 8q11.2 and considered to be an orphan gene. Our Southern blot-EcoRI-RFLP studies in normal individuals and in patients with rheumatoid arthritis (RA) or with systemic lupus erythematosus (SLE), using a specific probe for the IGLV8 gene family (probe pVL8, EMBL accession No. X75424), have revealed the two monomorphic genomic fragments containing the IGLV8 genes, i.e., the 3.7-kb fragment from chromosome 22q11.1 and the 8.0-kb fragment from 8q11.2, both occurring at 100% frequency (103 normal individuals, 48 RA and 28 SLE patients analyzed), but absence of the 6.0-kb IGLV8 polymorphic RFLP allele in all RA or SLE patients. As expected, the frequency of the 6.0-kb allele among the normal individuals was 10%. These findings suggest an association between the absence of the 6.0-kb EcoRI fragment and rheumatoid arthritis and systemic lupus erythematosus.

An LMS style variable tap-length algorithm for structure adaptation

Searching for the optimum tap-length that best balances the complexity and steady-state performance of an adaptive filter has attracted attention recently. Among existing algorithms that can be found in the literature, two of which, namely the segmented filter (SF) and gradient descent (GD) algorithms, are of particular interest as they can search for the optimum tap-length quickly. In this paper, at first, we carefully compare the SF and GD algorithms and show that the two algorithms are equivalent in performance under some constraints, but each has advantages/disadvantages relative to the other. Then, we propose an improved variable tap-length algorithm using the concept of the pseudo fractional tap-length (FT). Updating the tap-length with instantaneous errors in a style similar to that used in the stochastic gradient [or least mean squares (LMS)] algorithm, the proposed FT algorithm not only retains the advantages from both the SF and the GD algorithms but also has significantly less complexity than existing algorithms. Both performance analysis and numerical simulations are given to verify the new proposed algorithm.

Economic design of two-stage (X)over-bar charts: the Markov chain approach

When the (X) over bar chart is in use, samples are regularly taken from the process, and their means are plotted on the chart. In some cases, it is too expensive to obtain the X values, but not the values of a correlated variable Y. This paper presents a model for the economic design of a two-stage control chart, that is. a control chart based on both performance (X) and surrogate (Y) variables. The process is monitored by the surrogate variable until it signals an out-of-control behavior, and then a switch is made to the (X) over bar chart. The (X) over bar chart is built with central, warning. and action regions. If an X sample mean falls in the central region, the process surveillance returns to the (Y) over bar chart. Otherwise. The process remains under the (X) over bar chart's surveillance until an (X) over bar sample mean falls outside the control limits. The search for an assignable cause is undertaken when the performance variable signals an out-of-control behavior. In this way, the two variables, are used in an alternating fashion. The assumption of an exponential distribution to describe the length of time the process remains in control allows the application of the Markov chain approach for developing the cost function. A study is performed to examine the economic advantages of using performance and surrogate variables. (C) 2003 Elsevier B.V. All rights reserved.

Effect of the length of alkyl side chains in the electronic structure of conjugated polymers

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Partially Observed Markov Random Fields Are Variable Neighborhood Random Fields

The present paper has two goals. First to present a natural example of a new class of random fields which are the variable neighborhood random fields. The example we consider is a partially observed nearest neighbor binary Markov random field. The second goal is to establish sufficient conditions ensuring that the variable neighborhoods are almost surely finite. We discuss the relationship between the almost sure finiteness of the interaction neighborhoods and the presence/absence of phase transition of the underlying Markov random field. In the case where the underlying random field has no phase transition we show that the finiteness of neighborhoods depends on a specific relation between the noise level and the minimum values of the one-point specification of the Markov random field. The case in which there is phase transition is addressed in the frame of the ferromagnetic Ising model. We prove that the existence of infinite interaction neighborhoods depends on the phase.

Space trajectories optimization using variable-chromosome-length genetic algorithms

The problem of optimal design of a multi-gravity-assist space trajectories, with free number of deep space maneuvers (MGADSM) poses multi-modal cost functions. In the general form of the problem, the number of design variables is solution dependent. To handle global optimization problems where the number of design variables varies from one solution to another, two novel genetic-based techniques are introduced: hidden genes genetic algorithm (HGGA) and dynamic-size multiple population genetic algorithm (DSMPGA). In HGGA, a fixed length for the design variables is assigned for all solutions. Independent variables of each solution are divided into effective and ineffective (hidden) genes. Hidden genes are excluded in cost function evaluations. Full-length solutions undergo standard genetic operations. In DSMPGA, sub-populations of fixed size design spaces are randomly initialized. Standard genetic operations are carried out for a stage of generations. A new population is then created by reproduction from all members based on their relative fitness. The resulting sub-populations have different sizes from their initial sizes. The process repeats, leading to increasing the size of sub-populations of more fit solutions. Both techniques are applied to several MGADSM problems. They have the capability to determine the number of swing-bys, the planets to swing by, launch and arrival dates, and the number of deep space maneuvers as well as their locations, magnitudes, and directions in an optimal sense. The results show that solutions obtained using the developed tools match known solutions for complex case studies. The HGGA is also used to obtain the asteroids sequence and the mission structure in the global trajectory optimization competition (GTOC) problem. As an application of GA optimization to Earth orbits, the problem of visiting a set of ground sites within a constrained time frame is solved. The J2 perturbation and zonal coverage are considered to design repeated Sun-synchronous orbits. Finally, a new set of orbits, the repeated shadow track orbits (RSTO), is introduced. The orbit parameters are optimized such that the shadow of a spacecraft on the Earth visits the same locations periodically every desired number of days.

Encapsulation of lipopeptides within liposomes: Effect of number of lipid chains, chain length and method of liposome preparation

The purpose of this study was to systematically investigate the effect of lipid chain length and number of lipid chains present on lipopeptides on their ability to be incorporated within liposomes. The peptide KAVYNFATM was synthesized and conjugated to lipoamino acids having acyl chain lengths of C-8, C-12 and C-16. The C-12 construct was also prepared in the monomeric, dimeric and trimeric form. Liposomes were prepared by two techniques: hydration of dried lipid films (Bangham method) and hydration of freeze-dried monophase systems. Encapsulation of lipopeptide within liposomes prepared by hydration of dried lipid films was incomplete in all cases ranging from an entrapment efficiency of 70% for monomeric lipoamino acids at a 5% (w/w) loading to less than 20% for di- and trimeric forms at loadings of 20% (w/w). The incomplete entrapment of lipopeptides within liposomes appeared to be a result of the different solubilities of the lipopeptide and the phospholipids in the solvent used for the preparation of the lipid film. In contrast, encapsulation of lipopeptide within liposomes prepared by hydration of freeze-dried monophase systems was high, even up to a loading of 20% (w/w) and was much less affected by the acyl chain length and number than when liposomes were prepared by hydration of dried lipid films. Freeze drying of monophase systems is better at maintaining a molecular dispersion of the lipopeptide within the solid phospholipid matrix compared to preparation of lipid film by evaporation, particularly if the solubility of the lipopeptide in solvents is markedly different from that of the polar lipids used for liposome preparation. Consequently, upon hydration, the lipopeptide is more efficiently intercalated within the phospholipid bilayers. (C) 2005 Elsevier B.V. All rights reserved.