Optimal Capital Requirements in Financial Networks with Fire Sales

I explore and analyze a problem of finding the socially optimal capital requirements for financial institutions considering two distinct channels of contagion: direct exposures among the institutions, as represented by a network and fire sales externalities, which reflect the negative price impact of massive liquidation of assets.These two channels amplify shocks from individual financial institutions to the financial system as a whole and thus increase the risk of joint defaults amongst the interconnected financial institutions; this is often referred to as systemic risk. In the model, there is a trade-off between reducing systemic risk and raising the capital requirements of the financial institutions. The policymaker considers this trade-off and determines the optimal capital requirements for individual financial institutions. I provide a method for finding and analyzing the optimal capital requirements that can be applied to arbitrary network structures and arbitrary distributions of investment returns.

In particular, I first consider a network model consisting only of direct exposures and show that the optimal capital requirements can be found by solving a stochastic linear programming problem. I then extend the analysis to financial networks with default costs and show the optimal capital requirements can be found by solving a stochastic mixed integer programming problem. The computational complexity of this problem poses a challenge, and I develop an iterative algorithm that can be efficiently executed. I show that the iterative algorithm leads to solutions that are nearly optimal by comparing it with lower bounds based on a dual approach. I also show that the iterative algorithm converges to the optimal solution.

Finally, I incorporate fire sales externalities into the model. In particular, I am able to extend the analysis of systemic risk and the optimal capital requirements with a single illiquid asset to a model with multiple illiquid assets. The model with multiple illiquid assets incorporates liquidation rules used by the banks. I provide an optimization formulation whose solution provides the equilibrium payments for a given liquidation rule.

I further show that the socially optimal capital problem using the ``socially optimal liquidation" and prioritized liquidation rules can be formulated as a convex and convex mixed integer problem, respectively. Finally, I illustrate the results of the methodology on numerical examples and

discuss some implications for capital regulation policy and stress testing.

AN ECONOMIC ANALYSIS OF THE ADDITION OF BEVACIZUMAB TO STANDARD CHEMOTHERAPY IN PATIENTS WITH MALIGNANT PLEURAL MESOTHELIOMA

Thesis (Master's)--University of Washington, 2016-08

Machine learning and data decompositions for complex networked dynamical systems

Thesis (Ph.D.)--University of Washington, 2016-08

Spatio-temporal filtering properties of a dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework

The spike-diffuse-spike (SDS) model describes a passive dendritic tree with active dendritic spines. Spine-head dynamics is modeled with a simple integrate-and-fire process, whilst communication between spines is mediated by the cable equation. In this paper we develop a computational framework that allows the study of multiple spiking events in a network of such spines embedded on a simple one-dimensional cable. In the first instance this system is shown to support saltatory waves with the same qualitative features as those observed in a model with Hodgkin-Huxley kinetics in the spine-head. Moreover, there is excellent agreement with the analytically calculated speed for a solitary saltatory pulse. Upon driving the system with time varying external input we find that the distribution of spines can play a crucial role in determining spatio-temporal filtering properties. In particular, the SDS model in response to periodic pulse train shows a positive correlation between spine density and low-pass temporal filtering that is consistent with the experimental results of Rose and Fortune [1999, Mechanisms for generating temporal filters in the electrosensory system. The Journal of Experimental Biology 202, 1281-1289]. Further, we demonstrate the robustness of observed wave properties to natural sources of noise that arise both in the cable and the spine-head, and highlight the possibility of purely noise induced waves and coherent oscillations.

A model of macadamia with application to pruning in orchards

A self-organising model of macadamia, expressed using L-Systems, was used to explore aspects of canopy management. A small set of parameters control the basic architecture of the model, with a high degree of self-organisation occurring to determine the fate and growth of buds. Light was sensed at the leaf level and used to represent vigour and accumulated basipetally. Buds also sensed light so as to provide demand in the subsequent redistribution of the vigour. Empirical relationships were derived from a set of 24 completely digitised trees after conversion to multiscale tree graphs (MTG) and analysis with the OpenAlea software library. The ability to write MTG files was embedded within the model so that various tree statistics could be exported for each run of the model. To explore the parameter space a series of runs was completed using a high-throughput computing platform. When combined with MTG generation and analysis with OpenAlea it provided a convenient way in which thousands of simulations could be explored. We allowed the model trees to develop using self-organisation and simulated cultural practices such as hedging, topping, removal of the leader and limb removal within a small representation of an orchard. The model provides insight into the impact of these practices on potential for growth and the light distribution within the canopy and to the orchard floor by coupling the model with a path-tracing program to simulate the light environment. The lessons learnt from this will be applied to other evergreen, tropical fruit and nut trees.

A deformation model of flexible, high area-to-mass ratio debris under perturbations and validation method

A new type of space debris was recently discovered by Schildknecht in near -geosynchronous orbit (GEO). These objects were later identified as exhibiting properties associated with High Area-to-Mass ratio (HAMR) objects. According to their brightness magnitudes (light curve), high rotation rates and composition properties (albedo, amount of specular and diffuse reflection, colour, etc), it is thought that these objects are multilayer insulation (MLI). Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that their shapes are easily deformed leading to changes in the Area-to-Mass ratio (AMR) over time. This thesis proposes a simple effective flexible model of the thin, deformable membrane with two different methods. Firstly, this debris is modelled with Finite Element Analysis (FEA) by using Bernoulli-Euler theory called “Bernoulli model”. The Bernoulli model is constructed with beam elements consisting 2 nodes and each node has six degrees of freedom (DoF). The mass of membrane is distributed in beam elements. Secondly, the debris based on multibody dynamics theory call “Multibody model” is modelled as a series of lump masses, connected through flexible joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account with lump masses in the joints. The dynamic equations for the masses, including the constraints defined by the connecting rigid rod, are derived using fundamental Newtonian mechanics. The physical properties of both flexible models required by the models (membrane density, reflectivity, composition, etc.), are assumed to be those of multilayer insulation. Both flexible membrane models are then propagated together with classical orbital and attitude equations of motion near GEO region to predict the orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field, luni-solar gravitational fields and self-shadowing effect. These results are then compared to two rigid body models (cannonball and flat rigid plate). In this investigation, when comparing with a rigid model, the evolutions of orbital elements of the flexible models indicate the difference of inclination and secular eccentricity evolutions, rapid irregular attitude motion and unstable cross-section area due to a deformation over time. Then, the Monte Carlo simulations by varying initial attitude dynamics and deformed angle are investigated and compared with rigid models over 100 days. As the results of the simulations, the different initial conditions provide unique orbital motions, which is significantly different in term of orbital motions of both rigid models. Furthermore, this thesis presents a methodology to determine the material dynamic properties of thin membranes and validates the deformation of the multibody model with real MLI materials. Experiments are performed in a high vacuum chamber (10-4 mbar) replicating space environment. A thin membrane is hinged at one end but free at the other. The free motion experiment, the first experiment, is a free vibration test to determine the damping coefficient and natural frequency of the thin membrane. In this test, the membrane is allowed to fall freely in the chamber with the motion tracked and captured through high velocity video frames. A Kalman filter technique is implemented in the tracking algorithm to reduce noise and increase the tracking accuracy of the oscillating motion. The forced motion experiment, the last test, is performed to determine the deformation characteristics of the object. A high power spotlight (500-2000W) is used to illuminate the MLI and the displacements are measured by means of a high resolution laser sensor. Finite Element Analysis (FEA) and multibody dynamics of the experimental setups are used for the validation of the flexible model by comparing with the experimental results of displacements and natural frequencies.

Investigating assistive technology to support memory for people with cognitive impairments

Technologies such as automobiles or mobile phones allow us to perform beyond our physical capabilities and travel faster or communicate over long distances. Technologies such as computers and calculators can also help us perform beyond our mental capabilities by storing and manipulating information that we would be unable to process or remember. In recent years there has been a growing interest in assistive technology for cognition (ATC) which can help people compensate for cognitive impairments. The aim of this thesis was to investigate ATC for memory to help people with memory difficulties which impacts independent functioning during everyday life. Chapter one argues that using both neuropsychological and human computing interaction theory and approaches is crucial when developing and researching ATC. Chapter two describes a systematic review and meta-analysis of studies which tested technology to aid memory for groups with ABI, stroke or degenerative disease. Good evidence was found supporting the efficacy of prompting devices which remind the user about a future intention at a set time. Chapter three looks at the prevalence of technologies and memory aids in current use by people with ABI and dementia and the factors that predicted this use. Pre-morbid use of technology, current use of non-tech aids and strategies and age (ABI group only) were the best predictors of this use. Based on the results, chapter four focuses on mobile phone based reminders for people with ABI. Focus groups were held with people with memory impairments after ABI and ABI caregivers (N=12) which discussed the barriers to uptake of mobile phone based reminding. Thematic analysis revealed six key themes that impact uptake of reminder apps; Perceived Need, Social Acceptability, Experience/Expectation, Desired Content and Functions, Cognitive Accessibility and Sensory/Motor Accessibility. The Perceived need theme described the difficulties with insight, motivation and memory which can prevent people from initially setting reminders on a smartphone. Chapter five investigates the efficacy and acceptability of unsolicited prompts (UPs) from a smartphone app (ForgetMeNot) to encourage people with ABI to set reminders. A single-case experimental design study evaluated use of the app over four weeks by three people with severe ABI living in a post-acute rehabilitation hospital. When six UPs were presented through the day from ForgetMeNot, daily reminder-setting and daily memory task completion increased compared to when using the app without the UPs. Chapter six investigates another barrier from chapter 4 – cognitive and sensory accessibility. A study is reported which shows that an app with ‘decision tree’ interface design (ApplTree) leads to more accurate reminder setting performance with no compromise of speed or independence (amount of guidance required) for people with ABI (n=14) compared to a calendar based interface. Chapter seven investigates the efficacy of a wearable reminding device (smartwatch) as a tool for delivering reminders set on a smartphone. Four community dwelling participants with memory difficulties following ABI were included in an ABA single case experimental design study. Three of the participants successfully used the smartwatch throughout the intervention weeks and these participants gave positive usability ratings. Two participants showed improved memory performance when using the smartwatch and all participants had marked decline in memory performance when the technology was removed. Chapter eight is a discussion which highlights the implications of these results for clinicians, researchers and designers.

Pricing derivatives with stochastic volatility

This Ph.D. thesis contains 4 essays in mathematical finance with a focus on pricing Asian option (Chapter 4), pricing futures and futures option (Chapter 5 and Chapter 6) and time dependent volatility in futures option (Chapter 7). In Chapter 4, the applicability of the Albrecher et al.(2005)'s comonotonicity approach was investigated in the context of various benchmark models for equities and com- modities. Instead of classical Levy models as in Albrecher et al.(2005), the focus is the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and the Schwartz (1997) two-factor model. It is shown that the method delivers rather tight upper bounds for the prices of Asian Options in these models and as a by-product delivers super-hedging strategies which can be easily implemented. In Chapter 5, two types of three-factor models were studied to give the value of com- modities futures contracts, which allow volatility to be stochastic. Both these two models have closed-form solutions for futures contracts price. However, it is shown that Model 2 is better than Model 1 theoretically and also performs very well empiri- cally. Moreover, Model 2 can easily be implemented in practice. In comparison to the Schwartz (1997) two-factor model, it is shown that Model 2 has its unique advantages; hence, it is also a good choice to price the value of commodity futures contracts. Fur- thermore, if these two models are used at the same time, a more accurate price for commodity futures contracts can be obtained in most situations. In Chapter 6, the applicability of the asymptotic approach developed in Fouque et al.(2000b) was investigated for pricing commodity futures options in a Schwartz (1997) multi-factor model, featuring both stochastic convenience yield and stochastic volatility. It is shown that the zero-order term in the expansion coincides with the Schwartz (1997) two-factor term, with averaged volatility, and an explicit expression for the first-order correction term is provided. With empirical data from the natural gas futures market, it is also demonstrated that a significantly better calibration can be achieved by using the correction term as compared to the standard Schwartz (1997) two-factor expression, at virtually no extra effort. In Chapter 7, a new pricing formula is derived for futures options in the Schwartz (1997) two-factor model with time dependent spot volatility. The pricing formula can also be used to find the result of the time dependent spot volatility with futures options prices in the market. Furthermore, the limitations of the method that is used to find the time dependent spot volatility will be explained, and it is also shown how to make sure of its accuracy.

Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models

The presence of gap junction coupling among neurons of the central nervous systems has been appreciated for some time now. In recent years there has been an upsurge of interest from the mathematical community in understanding the contribution of these direct electrical connections between cells to large-scale brain rhythms. Here we analyze a class of exactly soluble single neuron models, capable of producing realistic action potential shapes, that can be used as the basis for understanding dynamics at the network level. This work focuses on planar piece-wise linear models that can mimic the firing response of several different cell types. Under constant current injection the periodic response and phase response curve (PRC) is calculated in closed form. A simple formula for the stability of a periodic orbit is found using Floquet theory. From the calculated PRC and the periodic orbit a phase interaction function is constructed that allows the investigation of phase-locked network states using the theory of weakly coupled oscillators. For large networks with global gap junction connectivity we develop a theory of strong coupling instabilities of the homogeneous, synchronous and splay state. For a piece-wise linear caricature of the Morris-Lecar model, with oscillations arising from a homoclinic bifurcation, we show that large amplitude oscillations in the mean membrane potential are organized around such unstable orbits.

Mode locking in a spatially extended neuron model: active soma and compartmental tree

Understanding the mode-locked response of excitable systems to periodic forcing has important applications in neuroscience. For example it is known that spatially extended place cells in the hippocampus are driven by the theta rhythm to generate a code conveying information about spatial location. Thus it is important to explore the role of neuronal dendrites in generating the response to periodic current injection. In this paper we pursue this using a compartmental model, with linear dynamics for each compartment, coupled to an active soma model that generates action potentials. By working with the piece-wise linear McKean model for the soma we show how the response of the whole neuron model (soma and dendrites) can be written in closed form. We exploit this to construct a stroboscopic map describing the response of the spatially extended model to periodic forcing. A linear stability analysis of this map, together with a careful treatment of the non-differentiability of the soma model, allows us to construct the Arnol'd tongue structure for 1:q states (one action potential for q cycles of forcing). Importantly we show how the presence of quasi-active membrane in the dendrites can influence the shape of tongues. Direct numerical simulations confirm our theory and further indicate that resonant dendritic membrane can enlarge the windows in parameter space for chaotic behavior. These simulations also show that the spatially extended neuron model responds differently to global as opposed to point forcing. In the former case spatio-temporal patterns of activity within an Arnol'd tongue are standing waves, whilst in the latter they are traveling waves.

Exchange rate dynamics, structural breaks, and central bank interventions in Colombia

We evaluate the effectiveness of the Colombian Central Bank´s interventions in the foreign exchange market during the period 2000 to 2014 -- We examine the stochastic process that describes the exchange rate, with a focus on the detection of structural breaks or unit roots in the data to determine whether the Central Bank´s interventions were effective -- We find that the exchange rate can be described either by a random walk or by a trend-stationary model with multiple breaks -- In neither cases do we find any evidence that the exchange rate was affected by the Central Bank interventions

RGS14 (414)-mediated prevention of an episodic memory loss: a study of molecular mechanism

A large proportion of human populations suffer memory impairments either caused by normal aging or afflicted by diverse neurological and neurodegenerative diseases. Memory enhancers and other drugs tested so far against memory loss have failed to produce therapeutic efficacy in clinical trials and thus, there is a need to find remedy for this mental disorder. In search for cure of memory loss, our laboratory discovered a robust memory enhancer called RGS14(414). A treatment in brain with its gene produces an enduring effect on memory that lasts for lifetime of rats. Therefore, current thesis work was designed to investigate whether RGS14(414) treatment can prevent memory loss and furthermore, explore through biological processes responsible for RGS-mediated memory enhancement. We found that RGS14(414) gene treatment prevented episodic memory loss in rodent models of normal aging and Alzheimer´s disease. A memory loss was observed in normal rats at 18 months of age; however, when they were treated with RGS14(414) gene at 3 months of age, they abrogated this deficit and their memory remained intact till the age of 22 months. In addition to normal aging rats, effect of memory enhancer treatment in mice model of Alzheimer´s disease (AD-mice) produced a similar effect. AD-mice subjected to treatment with RGS14(414) gene at the age of 2 months, a period when memory was intact, showed not only a prevention in memory loss observed at 4 months of age but also they were able to maintain normal memory after 6 months of the treatment. We posit that long-lasting effect on memory enhancement and prevention of memory loss mediated through RGS14(414) might be due to a permanent structural change caused by a surge in neuronal connections and enhanced neuronal remodeling, key processes for long-term memory formation. A neuronal arborization analysis of both pyramidal and non-pyramidal neurons in brain of RGS14(414)-treated rats exhibited robust rise in neurites outgrowth of both kind of cells, and an increment in number of branching from the apical dendrite of pyramidal neurons, reaching to almost three times of the control animals. To further understand of underlying mechanism by which RGS14(414) induces neuronal arborization, we investigated into neurotrophic factors. We observed that RGS14 treatment induces a selective increase in BDNF. Role of BDNF in neuronal arborization, as well as its implication in learning and memory processes is well described. In addition, our results showing a dynamic expression pattern of BDNF during ORM processing that overlapped with memory consolidation further support the idea of the implication of this neurotrophin in formation of long-term memory in RGS-animals. On the other hand, in studies of expression profiling of RGS-treated animals, we have demonstrated that 14-3-3ζ protein displays a coherent relationship to RGS-mediated ORM enhancement. Recent studies have demonstrated that the interaction of receptor for activated protein kinase 1 (RACK1) with 14-3-3ζ is essential for its nuclear translocation, where RACK1-14-3-3ζ complex binds at promotor IV region of BDNF and promotes an increase in BDNF gene transcription. These observations suggest that 14-3-3ζ might regulate the elevated level of BDNF seen in RGS14(414) gene treated animals. Therefore, it seems that RGS-mediated surge in 14-3-3ζ causes elevated BDNF synthesis needed for neuronal arborization and enhanced ORM. The prevention of memory loss might be mediated through a restoration in BDNF and 14-3-3ζ protein levels, which are significantly decreased in aging and Alzheimer’s disease. Additionally, our results demonstrate that RGS14(414) treatment could be a viable strategy against episodic memory loss.

Essays on Emissions Trading Markets

This dissertation is a collection of three economics essays on different aspects of carbon emission trading markets. The first essay analyzes the dynamic optimal emission control strategies of two nations. With a potential to become the largest buyer under the Kyoto Protocol, the US is assumed to be a monopsony, whereas with a large number of tradable permits on hand Russia is assumed to be a monopoly. Optimal costs of emission control programs are estimated for both the countries under four different market scenarios: non-cooperative no trade, US monopsony, Russia monopoly, and cooperative trading. The US monopsony scenario is found to be the most Pareto cost efficient. The Pareto efficient outcome, however, would require the US to make side payments to Russia, which will even out the differences in the cost savings from cooperative behavior. The second essay analyzes the price dynamics of the Chicago Climate Exchange (CCX), a voluntary emissions trading market. By examining the volatility in market returns using AR-GARCH and Markov switching models, the study associates the market price fluctuations with two different political regimes of the US government. Further, the study also identifies a high volatility in the returns few months before the market collapse. Three possible regulatory and market-based forces are identified as probable causes of market volatility and its ultimate collapse. Organizers of other voluntary markets in the US and worldwide may closely watch for these regime switching forces in order to overcome emission market crashes. The third essay compares excess skewness and kurtosis in carbon prices between CCX and EU ETS (European Union Emission Trading Scheme) Phase I and II markets, by examining the tail behavior when market expectations exceed the threshold level. Dynamic extreme value theory is used to find out the mean price exceedence of the threshold levels and estimate the risk loss. The calculated risk measures suggest that CCX and EU ETS Phase I are extremely immature markets for a risk investor, whereas EU ETS Phase II is a more stable market that could develop as a mature carbon market in future years.

Does Final Energy Demand in Portugal Exhibit Long Memory? A Fractional Integration Analysis

In this paper, we measure the degree of fractional integration in final energy demand in Portugal using an ARFIMA model with and without adjustments for seasonality. We consider aggregate energy demand as well as final demand for petroleum, electricity, coal, and natural gas. Our findings suggest the presence of long memory in all of the components of energy demand. All fractional-difference parameters are positive and lower than 0.5 indicating that the series are stationary, although with mean reversion patterns slower than in the typical short-run processes. These results have important implications for the design of energy policies. As a result of the long-memory in final energy demand, the effects of temporary policy shocks will tend to disappear slowly. This means that even transitory shocks have long lasting effects. Given the temporary nature of these effects, however, permanent effects on final energy demand require permanent policies. This is unlike what would be suggested by the more standard, but much more limited, unit root approach, which would incorrectly indicate that even transitory policies would have permanent effects

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.