pwc-archive/papers-with-abstracts huggingface dataset:
The Long Bond, Long Forward Measure and Long-Term Factorization in Heath-Jarrow-Morton Models
Date: 2017-07-27 00:00:00

This paper proves existence of the long bond, long forward measure and
long-term factorization of the stochastic discount factor (SDF) of Alvarez and
Jermann (2005) and Hansen and Scheinkman (2009) in Heath-Jarrow-Morton (HJM)
models in the function space framework of Filipovic (2001). A sufficient
condition on the weight in the Hilbert space of forward rate volatility curves
is given that ensures existence of the long bond volatility process, the long
bond process and the long-term factorization of the SDF into discounting at the
rate of return on the long bond and a martingale component defining the long
forward measure, the long-term limit of T-forward measures.
Sharpe portfolio using a cross-efficiency evaluation
Date: 2016-10-11 00:00:00

The Sharpe ratio is a way to compare the excess returns (over the risk free
asset) of portfolios for each unit of volatility that is generated by a
portfolio. In this paper we introduce a robust Sharpe ratio portfolio under the
assumption that the risk free asset is unknown. We propose a robust portfolio
that maximizes the Sharpe ratio when the risk free asset is unknown, but is
within a given interval. To compute the best Sharpe ratio portfolio all the
Sharpe ratios for any risk free asset are considered and compared by using the
so-called cross-efficiency evaluation. An explicit expression of the
Cross-Eficiency Sharpe ratio portfolio is presented when short selling is
allowed.
Exponential utility maximization under model uncertainty for unbounded endowments
Date: 2019-02-10 00:00:00

We consider the robust exponential utility maximization problem in discrete
time: An investor maximizes the worst case expected exponential utility with
respect to a family of nondominated probabilistic models of her endowment by
dynamically investing in a financial market, and statically in available
options. We show that, for any measurable random endowment (regardless of
whether the problem is finite or not) an optimal strategy exists, a dual
representation in terms of (calibrated) martingale measures holds true, and
that the problem satisfies the dynamic programming principle (in case of no
options). Further it is shown that the value of the utility maximization
problem converges to the robust superhedging price as the risk aversion
parameter gets large, and examples of nondominated probabilistic models are
discussed.
Sources of false positives and false negatives in the STATCHECK algorithm: Reply to Nuijten et al. (2016)
Date: 2017-11-23 00:00:00
Tasks: valid

STATCHECK is an R algorithm designed to scan papers automatically for
inconsistencies between test statistics and their associated p values (Nuijten
et al., 2016). The goal of this comment is to point out an important and
well-documented flaw in this busily applied algorithm: It cannot handle
corrected p values. As a result, statistical tests applying appropriate
corrections to the p value (e.g., for multiple tests, post-hoc tests,
violations of assumptions, etc.) are likely to be flagged as reporting
inconsistent statistics, whereas papers omitting necessary corrections are
certified as correct. The STATCHECK algorithm is thus valid for only a subset
of scientific papers, and conclusions about the quality or integrity of
statistical reports should never be based solely on this program.
Information inefficiency in a random linear economy model
Date: 2016-10-10 00:00:00
Tasks: model

We study the effects of introducing information inefficiency in a model for a
random linear economy with a representative consumer. This is done by
considering statistical, instead of classical, economic general equilibria.
Employing two different approaches we show that inefficiency increases the
consumption set of a consumer but decreases her expected utility. In this
scenario economic activity grows while welfare shrinks, that is the opposite of
the behavior obtained by considering a rational consumer.
Bifurcation analysis and global dynamics of a mathematical model of antibiotic resistance in hospitals
Date: 2016-09-27 00:00:00

Antibiotic-resistant bacteria has posed a grave threat to public health by
causing a number of nosocomial infections in hospitals. Mathematical models
have been used to study the transmission of antibiotic-resistant bacteria
within a hospital and the measures to control antibiotic resistance in
nosocomial pathogens. Studies presented in \cite{LBL,LB} have shown great value
in understanding the transmission of antibiotic-resistant bacteria in a
hospital. However, their results are limited to numerical simulations of a few
different scenarios without analytical analysis of the models in all
biologically feasible parameter regions. Bifurcation analysis and
identification of the global stability conditions are necessary to assess the
interventions which are proposed to limit nosocomial infection and stem the
spread of antibiotic-resistant bacteria. In this paper we study the global
dynamics of the mathematical model of antibiotic resistance in hospitals in
\cite{LBL,LB}. The invasion reproduction number $\mathcal R_{ar}$ of
antibiotic-resistant bacteria is introduced. We give the relationship of
$\mathcal R_{ar}$ and two control reproduction numbers of sensitive bacteria
and resistant bacteria ($\mathcal R_{sc}$ and $\mathcal R_{rc}$). More
importantly, we prove that a backward bifurcation may occur at $\mathcal
R_{ar}=1$ when the model includes superinfection which is not mentioned in
\cite{LB}. That is, there exists a new threshold $\mathcal R_{ar}^c$, and if
$\mathcal R_{ar}^c<\mathcal R_{ar}<1$, then the system can have two interior
equilibria and it supports an interesting bistable phenomenon. This provides
critical information on controlling the antibiotic-resistance in a hospital.
Asset Pricing with Random Volatility
Date: 2018-09-19 00:00:00

This paper proposes to model asset price dynamics with a mixture of diffusion
processes where the instantaneous volatility of the underlying diffusion
process contains a random vector. The marginal probability distributions of the
proposed process can match exactly the risk-neutral distributions implied by
both spot vanilla options and forward start options. We can also derive the
explicit pricing formula for derivatives that have a closed-form solution under
Generalized Geometric Brownian Motion.
Systematic evaluation of a new combinatorial curvature for complex networks
Date: 2017-05-15 00:00:00

We have recently introduced Forman's discretization of Ricci curvature to the
realm of complex networks. Forman curvature is an edge-based measure whose
mathematical definition elegantly encapsulates the weights of nodes and edges
in a complex network. In this contribution, we perform a comparative analysis
of Forman curvature with other edge-based measures such as edge betweenness,
embeddedness and dispersion in diverse model and real networks. We find that
Forman curvature in comparison to embeddedness or dispersion is a better
indicator of the importance of an edge for the large-scale connectivity of
complex networks. Based on the definition of the Forman curvature of edges,
there are two natural ways to define the Forman curvature of nodes in a
network. In this contribution, we also examine these two possible definitions
of Forman curvature of nodes in diverse model and real networks. Based on our
empirical analysis, we find that in practice the unnormalized definition of the
Forman curvature of nodes with the choice of combinatorial node weights is a
better indicator of the importance of nodes in complex networks.
Administration Costs in the Management of Research Funds; A Case Study of a Public Fund for the Promotion of Industrial Innovation
Date: 2016-09-19 00:00:00
Tasks: Management, Marketing

Research funding agencies routinely use a proportion of their total revenues
to support internal administration and marketing costs. The ratio of
administration to total costs, referred to as the administration ratio, is
highly variable and within any single fund depends on many factors including
the number and average size of projects and the overall efficiency of the
funding agency. In this study, the standard agency activities have been
identified and used to develop a model of administration costs against expected
outcomes. In particular, the model has been designed to estimate the optimum
portfolio success rate and administration ratio as a function of a range of key
input variables including the project size, the complexity of proposal
evaluation and project management, the risk tolerance of the sponsor and the
targeted research domain.
Influence of Pok\'emon Go on Physical Activity: Study and Implications
Authors: Althoff Tim, White Ryen W., Horvitz Eric
Date: 2016-10-28 00:00:00

Physical activity helps people maintain a healthy weight and reduces the risk
for several chronic diseases. Although this knowledge is widely recognized,
adults and children in many countries around the world do not get recommended
amounts of physical activity. While many interventions are found to be
ineffective at increasing physical activity or reaching inactive populations,
there have been anecdotal reports of increased physical activity due to novel
mobile games that embed game play in the physical world. The most recent and
salient example of such a game is Pok\'emon Go, which has reportedly reached
tens of millions of users in the US and worldwide.
  We study the effect of Pok\'emon Go on physical activity through a
combination of signals from large-scale corpora of wearable sensor data and
search engine logs for 32 thousand users over a period of three months.
Pok\'emon Go players are identified through search engine queries and activity
is measured through accelerometry. We find that Pok\'emon Go leads to
significant increases in physical activity over a period of 30 days, with
particularly engaged users (i.e., those making multiple search queries for
details about game usage) increasing their activity by 1473 steps a day on
average, a more than 25% increase compared to their prior activity level
($p<10^{-15}$). In the short time span of the study, we estimate that Pok\'emon
Go has added a total of 144 billion steps to US physical activity. Furthermore,
Pok\'emon Go has been able to increase physical activity across men and women
of all ages, weight status, and prior activity levels showing this form of game
leads to increases in physical activity with significant implications for
public health. We find that Pok\'emon Go is able to reach low activity
populations while all four leading mobile health apps studied in this work
largely draw from an already very active population.
Neutral Aggregation in Finite Length Genotype space
Date: 2016-12-19 00:00:00

The advent of modern genome sequencing techniques allows for a more stringent
test of the neutrality hypothesis of Darwinian evolution, where all individuals
have the same fitness. Using the individual based model of Wright and Fisher,
we compute the amplitude of neutral aggregation in the genome space, i.e., the
probability of finding two individuals at genetic (hamming) distance k as a
function of genome size L, population size N and mutation probability per base
\nu. In well mixed populations, we show that for N\nu\textless{}1/L, neutral
aggregation is the dominant force and most individuals are found at short
genetic distances from each other. For N\nu\textgreater{}1 on the contrary,
individuals are randomly dispersed in genome space. The results are extended to
geographically dispersed population, where the controlling parameter is shown
to be a combination of mutation and migration probability. The theory we
develop can be used to test the neutrality hypothesis in various ecological and
evolutionary systems.
Mathematical modeling of local perfusion in large distensible microvascular networks
Date: 2016-09-28 00:00:00

Microvessels -blood vessels with diameter less than 200 microns- form large,
intricate networks organized into arterioles, capillaries and venules. In these
networks, the distribution of flow and pressure drop is a highly interlaced
function of single vessel resistances and mutual vessel interactions. In this
paper we propose a mathematical and computational model to study the behavior
of microcirculatory networks subjected to different conditions. The network
geometry is composed of a graph of connected straight cylinders, each one
representing a vessel. The blood flow and pressure drop across the single
vessel, further split into smaller elements, are related through a generalized
Ohm's law featuring a conductivity parameter, function of the vessel cross
section area and geometry, which undergo deformations under pressure loads. The
membrane theory is used to describe the deformation of vessel lumina, tailored
to the structure of thick-walled arterioles and thin-walled venules. In
addition, since venules can possibly experience negative transmural pressures,
a buckling model is also included to represent vessel collapse. The complete
model including arterioles, capillaries and venules represents a nonlinear
system of PDEs, which is approached numerically by finite element
discretization and linearization techniques. We use the model to simulate flow
in the microcirculation of the human eye retina, a terminal system with a
single inlet and outlet. After a phase of validation against experimental
measurements, we simulate the network response to different interstitial
pressure values. Such a study is carried out both for global and localized
variations of the interstitial pressure. In both cases, significant
redistributions of the blood flow in the network arise, highlighting the
importance of considering the single vessel behavior along with its position
and connectivity in the network.
Volatility Smile as Relativistic Effect
Date: 2017-02-20 00:00:00

We give an explicit formula for the probability distribution based on a
relativistic extension of Brownian motion. The distribution 1) is properly
normalized and 2) obeys the tower law (semigroup property), so we can construct
martingales and self-financing hedging strategies and price claims (options).
This model is a 1-constant-parameter extension of the Black-Scholes-Merton
model. The new parameter is the analog of the speed of light in Special
Relativity. However, in the financial context there is no "speed limit" and the
new parameter has the meaning of a characteristic diffusion speed at which
relativistic effects become important and lead to a much softer asymptotic
behavior, i.e., fat tails, giving rise to volatility smiles. We argue that a
nonlocal stochastic description of such (Levy) processes is inadequate and
discuss a local description from physics. The presentation is intended to be
pedagogical.
Honing Theory: A Complex Systems Framework for Creativity
Date: 2019-07-15 00:00:00
Tasks: Cultural Vocal Bursts Intensity Prediction

This paper proposes a theory of creativity, referred to as honing theory,
which posits that creativity fuels the process by which culture evolves through
communal exchange amongst minds that are self-organizing, self-maintaining, and
self-reproducing. According to honing theory, minds, like other selforganizing
systems, modify their contents and adapt to their environments to minimize
entropy. Creativity begins with detection of high psychological entropy
material, which provokes uncertainty and is arousalinducing. The creative
process involves recursively considering this material from new contexts until
it is sufficiently restructured that arousal dissipates. Restructuring involves
neural synchrony and dynamic binding, and may be facilitated by temporarily
shifting to a more associative mode of thought. A creative work may similarly
induce restructuring in others, and thereby contribute to the cultural
evolution of more nuanced worldviews. Since lines of cultural descent
connecting creative outputs may exhibit little continuity, it is proposed that
cultural evolution occurs at the level of self-organizing minds, outputs
reflect their evolutionary state. Honing theory addresses challenges not
addressed by other theories of creativity, such as the factors that guide
restructuring, and in what sense creative works evolve. Evidence comes from
empirical studies, an agent-based computational model of cultural evolution,
and a model of concept combination.
Feasible Invertibility Conditions for Maximum Likelihood Estimation for Observation-Driven Models
Date: 2016-10-10 00:00:00
Tasks: Time Series, Time Series Analysis

Invertibility conditions for observation-driven time series models often fail
to be guaranteed in empirical applications. As a result, the asymptotic theory
of maximum likelihood and quasi-maximum likelihood estimators may be
compromised. We derive considerably weaker conditions that can be used in
practice to ensure the consistency of the maximum likelihood estimator for a
wide class of observation-driven time series models. Our consistency results
hold for both correctly specified and misspecified models. The practical
relevance of the theory is highlighted in a set of empirical examples. We
further obtain an asymptotic test and confidence bounds for the unfeasible "
true " invertibility region of the parameter space.
Evolution of new regulatory functions on biophysically realistic fitness landscapes
Date: 2017-02-27 00:00:00
Tasks: Specificity

Regulatory networks consist of interacting molecules with a high degree of
mutual chemical specificity. How can these molecules evolve when their function
depends on maintenance of interactions with cognate partners and simultaneous
avoidance of deleterious "crosstalk" with non-cognate molecules? Although
physical models of molecular interactions provide a framework in which
co-evolution of network components can be analyzed, most theoretical studies
have focused on the evolution of individual alleles, neglecting the network. In
contrast, we study the elementary step in the evolution of gene regulatory
networks: duplication of a transcription factor followed by selection for TFs
to specialize their inputs as well as the regulation of their downstream genes.
We show how to coarse grain the complete, biophysically realistic
genotype-phenotype map for this process into macroscopic functional outcomes
and quantify the probability of attaining each. We determine which evolutionary
and biophysical parameters bias evolutionary trajectories towards fast
emergence of new functions and show that this can be greatly facilitated by the
availability of "promiscuity-promoting" mutations that affect TF specificity.
Optimal Download Cost of Private Information Retrieval for Arbitrary Message Length
Authors: Sun Hua, Jafar Syed A.
Date: 2016-10-10 00:00:00
Tasks: All, Information Retrieval, Retrieval

A private information retrieval scheme is a mechanism that allows a user to
retrieve any one out of $K$ messages from $N$ non-communicating replicated
databases, each of which stores all $K$ messages, without revealing anything
about the identity of the desired message index to any individual database. If
the size of each message is $L$ bits and the total download required by a PIR
scheme from all $N$ databases is $D$ bits, then $D$ is called the download cost
and the ratio $L/D$ is called an achievable rate. For fixed $K,N\in\mathbb{N}$,
the capacity of PIR, denoted by $C$, is the supremum of achievable rates over
all PIR schemes and over all message sizes, and was recently shown to be
$C=(1+1/N+1/N^2+\cdots+1/N^{K-1})^{-1}$. In this work, for arbitrary $K, N$, we
explore the minimum download cost $D_L$ across all PIR schemes (not restricted
to linear schemes) for arbitrary message lengths $L$ under arbitrary choices of
alphabet (not restricted to finite fields) for the message and download
symbols. If the same $M$-ary alphabet is used for the message and download
symbols, then we show that the optimal download cost in $M$-ary symbols is
$D_L=\lceil\frac{L}{C}\rceil$. If the message symbols are in $M$-ary alphabet
and the downloaded symbols are in $M'$-ary alphabet, then we show that the
optimal download cost in $M'$-ary symbols, $D_L\in\left\{\left\lceil
\frac{L'}{C}\right\rceil,\left\lceil \frac{L'}{C}\right\rceil-1,\left\lceil
\frac{L'}{C}\right\rceil-2\right\}$, where $L'= \lceil L \log_{M'} M\rceil$.
Dependent Defaults and Losses with Factor Copula Models
Date: 2018-01-17 00:00:00

We present a class of flexible and tractable static factor models for the
term structure of joint default probabilities, the factor copula models. These
high-dimensional models remain parsimonious with pair-copula constructions, and
nest many standard models as special cases. The loss distribution of a
portfolio of contingent claims can be exactly and efficiently computed when
individual losses are discretely supported on a finite grid. Numerical examples
study the key features affecting the loss distribution and multi-name credit
derivatives prices. An empirical exercise illustrates the flexibility of our
approach by fitting credit index tranche prices.
Option pricing with Legendre polynomials
Date: 2017-03-19 00:00:00

Here we develop an option pricing method based on Legendre series expansion
of the density function. The key insight, relying on the close relation of the
characteristic function with the series coefficients, allows to recover the
density function rapidly and accurately. Based on this representation for the
density function, approximations formulas for pricing European type options are
derived. To obtain highly accurate result for European call option, the
implementation involves integrating high degree Legendre polynomials against
exponential function. Some numerical instabilities arise because of serious
subtractive cancellations in its formulation (96) in proposition 7.1. To
overcome this difficulty, we rewrite this quantity as solution of a
second-order linear difference equation and solve it using a robust and stable
algorithm from Olver. Derivation of the pricing method has been accompanied by
an error analysis. Errors bounds have been derived and the study relies more on
smoothness properties which are not provided by the payoff? functions, but
rather by the density function of the underlying stochastic models. This is
particularly relevant for options pricing where the payoff of the contract are
generally not smooth functions. The numerical experiments on a class of models
widely used in quantitative finance show exponential convergence.
Characterizing variability in nonlinear recurrent neuronal networks
Date: 2016-10-10 00:00:00

In this note, we develop semi-analytical techniques to obtain the full
correlational structure of a stochastic network of nonlinear neurons described
by rate variables. Under the assumption that pairs of membrane potentials are
jointly Gaussian -- which they tend to be in large networks -- we obtain
deterministic equations for the temporal evolution of the mean firing rates and
the noise covariance matrix that can be solved straightforwardly given the
network connectivity. We also obtain spike count statistics such as Fano
factors and pairwise correlations, assuming doubly-stochastic action potential
firing. Importantly, our theory does not require fluctuations to be small, and
works for several biologically motivated, convex single-neuron nonlinearities.