pwc-archive/papers-with-abstracts huggingface dataset:
Hedging in a market with jumps - an FBSDE approach
Date: 2017-08-30 00:00:00

We propose a model for hedging in a market with jumps for a large investor.
The dynamics of the stock prices and the value process is governed by
forward-backward SDEs driven by Teugels martingales. Unlike known FBSDE market
models, ours accounts for jumps in stock prices. Moreover, it allows to find an
optimal hedging strategy.
Inferring selective constraint from population genomic data suggests recent regulatory turnover in the human brain
Date: 2015-11-22 00:00:00

The comparative genomics revolution of the past decade has enabled the
discovery of functional elements in the human genome via sequence comparison.
While that is so, an important class of elements, those specific to humans, is
entirely missed by searching for sequence conservation across species. Here we
present an analysis based on variation data among human genomes that utilizes a
supervised machine learning approach for the identification of human specific
purifying selection in the genome. Using only allele frequency information from
the complete low coverage 1000 Genomes Project dataset in conjunction with a
support vector machine trained from known functional and non-functional
portions of the genome, we are able to accurately identify portions of the
genome constrained by purifying selection. Our method identifies previously
known human-specific gains or losses of function and uncovers many novel
candidates. Candidate targets for gain and loss of function along the human
lineage include numerous putative regulatory regions of genes essential for
normal development of the central nervous system, including a significant
enrichment of gain of function events near neurotransmitter receptor genes.
These results are consistent with regulatory turnover being a key mechanism in
the evolution of human-specific characteristics of brain development. Finally,
we show that the majority of the genome is unconstrained by natural selection
currently, in agreement with what has been estimated from phylogenetic methods
but in sharp contrast to estimates based on transcriptomics or other
high-throughput functional methods.
The Recognizability of Individual Creative Styles Within and Across Domains
Date: 2019-06-30 00:00:00

We present a set of studies that tested the hypothesis that creative style is
recognizable within and across domains. Art students were shown two sets of
paintings, the first by five famous artists and the second by their art student
peers. For both sets, they guessed the creators of the works at above-chance
levels. In a similar study, creative writing students guessed at above-chance
levels which passages were written by which of five famous writers, and which
passages were written by which of their writing student peers. When creative
writing students were asked to produce works of art, they guessed at
above-chance levels which of their peers produced which artwork. Finally, art
students who were familiar with each other's paintings guessed at above-chance
levels which of their peers produced which non-painting artwork. The findings
support the hypothesis that creative styles are recognizable not just within
but also across domains. We suggest this is because all of an individual's
creative outputs are expressions of a particular underlying uniquely structured
self-organizing internal model of the world.
Five clarifications about cultural evolution
Date: 2019-06-30 00:00:00
Tasks: Cultural Vocal Bursts Intensity Prediction

This paper reviews and clarifies five misunderstandings about cultural
evolution identified by Henrich, Boyd, and Richerson (2008). First, cultural
representations are neither discrete nor continuous; they are distributed
across neurons that respond to microfeatures. This enables associations to be
made, and cultural change to be generated. Second, 'replicator dynamics' do not
ensure natural selection. The replicator notion does not capture the
distinction between actively interpreted self-assembly code and passively
copied self-description, which leads to a fundamental principle of natural
selection: inherited information is transmitted, whereas acquired information
is not. Third, this principle is violated in culture by the ubiquity of
acquired change. Moreover, biased transmission is less important to culture
than the creative processes by which novelty is generated. Fourth, there is no
objective basis for determining cultural fitness. Fifth, the necessity of
randomness is discussed. It is concluded that natural selection is
inappropriate as an explanatory framework for culture.
The Late-Pleistocene extinction of megafauna compared with the growth of human population
Date: 2017-11-23 00:00:00

Time-dependent distribution of the global extinction of megafauna is compared
with the growth of human population. There is no correlation between the two
processes. Furthermore, the size of human population and its growth rate were
far too small to have any significant impact on the environment and on the life
of megafauna.
A Boolean Gene Regulatory Model of heterosis and speciation
Date: 2015-03-23 00:00:00

Modelling genetic phenomena affecting biological traits is important for the
development of agriculture as it allows breeders to predict the potential of
breeding for certain traits. One such phenomenon is heterosis or hybrid vigor:
crossing individuals from genetically distinct populations often results in
improvements in quantitative traits, such as growth rate, biomass production
and stress resistance. Heterosis has become a very useful tool in global
agriculture, but its genetic basis remains controversial and its effects hard
to predict. We have taken a computational approach to studying heterosis,
developing a simulation of evolution, independent reassortment of alleles and
hybridization of Gene Regulatory Networks (GRNs) in a Boolean framework.
Fitness is measured as the ability of a network to respond to external inputs
in a pre-defined way. Our model reproduced common experimental observations on
heterosis using only biologically justified parameters. Hybrid vigor was
observed and its extent was seen to increase as parental populations diverged,
up until a point of sudden collapse of hybrid fitness. We also reproduce, for
the first time in a model, the fact that hybrid vigor cannot easily be fixed by
within a breeding line, currently an important limitation of the use of hybrid
crops. The simulation allowed us to study the effects of three standard models
for the genetic basis of heterosis and the level of detail in our model allows
us to suggest possible warning signs of the impending collapse of hybrid vigor
in breeding. In addition, the simulation provides a framework that can be
extended to study other aspects of heterosis and alternative evolutionary
scenarios.
Watterson estimators for Next Generation Sequencing: from trios to autopolyploids
Date: 2015-09-21 00:00:00

Several variations of the Watterson estimator of variability for Next
Generation Sequencing (NGS) data have been proposed in the literature. We
present a unified framework for generalized Watterson estimators based on
Maximum Composite Likelihood, which encompasses most of the existing
estimators. We propose this class of unbiased estimators as generalized
Watterson estimators for a large class of NGS data, including pools and trios.
We also discuss the relation with the estimators that have been proposed in the
literature and show that they admit two equivalent but seemingly different
forms, deriving a set of combinatorial identities as a byproduct. Finally, we
give a detailed treatment of Watterson estimators for single or multiple
autopolyploid individuals.
An Analysis of the 'Blind Variation and Selective Retention' Theory of Creativity
Date: 2019-06-30 00:00:00

Picasso's Guernica sketches continue to provide a fruitful testing ground for
examining and assessing the Blind Variation Selective Retention (BVSR) theory
of creativity. Nonmonotonicity--e.g. as indicated by a lack of similarity of
successive sketches--is not evidence of a selectionist process; Darwin's theory
explains adaptive change, not nonmonotonicity. Although the notion of blindness
originally implied randomness, it now encompasses phenomena that bias idea
generation, e.g. the influence of remote associations on sketch ideas. However,
for a selectionist framework is to be applicable, such biases must be
negligible, otherwise evolutionary change is attributed to those biases, not to
selection. The notion of 'variants' should not be applied to creativity;
without a mechanism of inheritance, there is no basis upon which to delineate,
for example, which sketch ideas are or are not variants of a given sketch idea.
The notion of selective retention is also problematic. Selection provides an
explanation when acquired change is not transmitted; it cannot apply to
Picasso's painting (or other creative acts) because his ideas acquired
modifications as he thought them through that were incorporated into paintings
and viewed by others. The generation of one sketch affects the criteria by
which the next is judged, so sequentially generated sketches cannot be treated
as members of a generation, and selected amongst. Although BVSR is
inappropriate as a theoretical framework for creativity, exploring to what
extent selectionism explains the generation of not just biological form but
masterpieces such as Picasso's Guernica is useful for gaining insight into
creativity.
Optimal Liquidity Provision
Date: 2015-02-26 00:00:00

A small investor provides liquidity at the best bid and ask prices of a limit
order market. For small spreads and frequent orders of other market
participants, we explicitly determine the investor's optimal policy and
welfare. In doing so, we allow for general dynamics of the mid price, the
spread, and the order flow, as well as for arbitrary preferences of the
liquidity provider under consideration.
A new financial metric for the art market
Date: 2015-07-27 00:00:00

This paper introduces a new financial metric for the art market. The metric
is based on the price per unit of area and is applicable to two-dimensional art
objects such as paintings.
Modeling capital gains taxes for trading strategies of infinite variation
Date: 2015-06-30 00:00:00

In this article we show that the payment flow of a linear tax on trading
gains from a security with a semimartingale price process can be constructed
for all c\`agl\`ad and adapted trading strategies. It is characterized as the
unique continuous extension of the tax payments for elementary strategies
w.r.t. the convergence "uniformly in probability". In this framework we prove
that under quite mild assumptions dividend payoffs have almost surely a
negative effect on investor's after-tax wealth if the riskless interest rate is
always positive.
Hedging in L\'evy Models and the Time Step Equivalent of Jumps
Date: 2017-07-24 00:00:00

We consider option hedging in a model where the underlying follows an
exponential L\'evy process. We derive approximations to the variance-optimal
and to some suboptimal strategies as well as to their mean squared hedging
errors. The results are obtained by considering the L\'evy model as a
perturbation of the Black-Scholes model. The approximations depend on the first
four moments of logarithmic stock returns in the L\'evy model and option price
sensitivities (greeks) in the limiting Black-Scholes model. We illustrate
numerically that our formulas work well for a variety of L\'evy models
suggested in the literature. From a theoretical point of view, it turns out
that jumps have a similar effect on hedging errors as discrete-time hedging in
the Black-Scholes model.
A novel spectral method for inferring general diploid selection from time series genetic data
Date: 2015-01-26 00:00:00
Tasks: Time Series, Time Series Analysis

The increased availability of time series genetic variation data from
experimental evolution studies and ancient DNA samples has created new
opportunities to identify genomic regions under selective pressure and to
estimate their associated fitness parameters. However, it is a challenging
problem to compute the likelihood of nonneutral models for the population
allele frequency dynamics, given the observed temporal DNA data. Here, we
develop a novel spectral algorithm to analytically and efficiently integrate
over all possible frequency trajectories between consecutive time points. This
advance circumvents the limitations of existing methods which require
fine-tuning the discretization of the population allele frequency space when
numerically approximating requisite integrals. Furthermore, our method is
flexible enough to handle general diploid models of selection where the
heterozygote and homozygote fitness parameters can take any values, while
previous methods focused on only a few restricted models of selection. We
demonstrate the utility of our method on simulated data and also apply it to
analyze ancient DNA data from genetic loci associated with coat coloration in
horses. In contrast to previous studies, our exploration of the full fitness
parameter space reveals that a heterozygote advantage form of balancing
selection may have been acting on these loci.
Cancer initiation with epistatic interactions between driver and passenger mutations
Date: 2015-04-13 00:00:00

We investigate the dynamics of cancer initiation in a mathematical model with
one driver mutation and several passenger mutations. Our analysis is based on a
multi type branching process: We model individual cells which can either divide
or undergo apoptosis. In case of a cell division, the two daughter cells can
mutate, which potentially confers a change in fitness to the cell. In contrast
to previous models, the change in fitness induced by the driver mutation
depends on the genetic context of the cell, in our case on the number of
passenger mutations. The passenger mutations themselves have no or only a very
small impact on the cell's fitness. While our model is not designed as a
specific model for a particular cancer, the underlying idea is motivated by
clinical and experimental observations in Burkitt Lymphoma. In this tumor, the
hallmark mutation leads to deregulation of the MYC oncogene which increases the
rate of apoptosis, but also the proliferation rate of cells. This increase in
the rate of apoptosis hence needs to be overcome by mutations affecting
apoptotic pathways, naturally leading to an epistatic fitness landscape. This
model shows a very interesting dynamical behavior which is distinct from the
dynamics of cancer initiation in the absence of epistasis. Since the driver
mutation is deleterious to a cell with only a few passenger mutations, there is
a period of stasis in the number of cells until a clone of cells with enough
passenger mutations emerges. Only when the driver mutation occurs in one of
those cells, the cell population starts to grow rapidly.
Limit theorems for nearly unstable Hawkes processes
Date: 2015-03-12 00:00:00
Tasks: Unity

Because of their tractability and their natural interpretations in term of
market quantities, Hawkes processes are nowadays widely used in high-frequency
finance. However, in practice, the statistical estimation results seem to show
that very often, only nearly unstable Hawkes processes are able to fit the data
properly. By nearly unstable, we mean that the $L^1$ norm of their kernel is
close to unity. We study in this work such processes for which the stability
condition is almost violated. Our main result states that after suitable
rescaling, they asymptotically behave like integrated Cox-Ingersoll-Ross
models. Thus, modeling financial order flows as nearly unstable Hawkes
processes may be a good way to reproduce both their high and low frequency
stylized facts. We then extend this result to the Hawkes-based price model
introduced by Bacry et al. [Quant. Finance 13 (2013) 65-77]. We show that under
a similar criticality condition, this process converges to a Heston model.
Again, we recover well-known stylized facts of prices, both at the
microstructure level and at the macroscopic scale.
Small-maturity asymptotics for the at-the-money implied volatility slope in L\'evy models
Date: 2016-05-30 00:00:00

We consider the at-the-money strike derivative of implied volatility as the
maturity tends to zero. Our main results quantify the behavior of the slope for
infinite activity exponential L\'evy models including a Brownian component. As
auxiliary results, we obtain asymptotic expansions of short maturity
at-the-money digital call options, using Mellin transform asymptotics. Finally,
we discuss when the at-the-money slope is consistent with the steepness of the
smile wings, as given by Lee's moment formula.
Asymptotic Glosten Milgrom equilibrium
Date: 2015-01-20 00:00:00

This paper studies the Glosten Milgrom model whose risky asset value admits
an arbitrary discrete distribution. Contrast to existing results on insider's
models, the insider's optimal strategy in this model, if exists, is not of
feedback type. Therefore a weak formulation of equilibrium is proposed. In this
weak formulation, the inconspicuous trade theorem still holds, but the
optimality for the insider's strategy is not enforced. However, the insider can
employ some feedback strategy whose associated expected profit is close to the
optimal value, when the order size is small. Moreover this discrepancy
converges to zero when the order size diminishes. The existence of such a weak
equilibrium is established, in which the insider's strategy converges to the
Kyle optimal strategy when the order size goes to zero.
Discriminative Measures for Comparison of Phylogenetic Trees
Date: 2015-10-20 00:00:00

In this paper we introduce and study three new measures for efficient
discriminative comparison of phylogenetic trees. The NNI navigation
dissimilarity $d_{nav}$ counts the steps along a "combing" of the Nearest
Neighbor Interchange (NNI) graph of binary hierarchies, providing an efficient
approximation to the (NP-hard) NNI distance in terms of "edit length". At the
same time, a closed form formula for $d_{nav}$ presents it as a weighted count
of pairwise incompatibilities between clusters, lending it the character of an
edge dissimilarity measure as well. A relaxation of this formula to a simple
count yields another measure on all trees --- the crossing dissimilarity
$d_{CM}$. Both dissimilarities are symmetric and positive definite (vanish only
between identical trees) on binary hierarchies but they fail to satisfy the
triangle inequality. Nevertheless, both are bounded below by the widely used
Robinson-Foulds metric and bounded above by a closely related true metric, the
cluster-cardinality metric $d_{CC}$. We show that each of the three proposed
new dissimilarities is computable in time $O(n^2)$ in the number of leaves $n$,
and conclude the paper with a brief numerical exploration of the distribution
over tree space of these dissimilarities in comparison with the Robinson-Foulds
metric and the more recently introduced matching-split distance.
Double Cascade Model of Financial Crises
Date: 2016-09-21 00:00:00
Tasks: model

The scope of financial systemic risk research encompasses a wide range of
interbank channels and effects, including asset correlation shocks, default
contagion, illiquidity contagion, and asset fire sales. This paper introduces a
financial network model that combines the default and liquidity stress
mechanisms into a "double cascade mapping". The progress and eventual result of
the crisis is obtained by iterating this mapping to its fixed point. Unlike
simpler models, this model can therefore quantify how illiquidity or default of
one bank influences the overall level of liquidity stress and default in the
system. Large-network asymptotic cascade mapping formulas are derived that can
be used for efficient network computations of the double cascade. Numerical
experiments then demonstrate that these asymptotic formulas agree qualitatively
with Monte Carlo results for large finite networks, and quantitatively except
when the initial system is placed in an exceptional "knife-edge" configuration.
The experiments clearly support the main conclusion that when banks respond to
liquidity stress by hoarding liquidity, then in the absence of asset fire
sales, the level of defaults in a financial network is negatively related to
the strength of bank liquidity hoarding and the eventual level of stress in the
network.
Unexpected links reflect the noise in networks
Date: 2015-09-26 00:00:00

Gene covariation networks are commonly used to study biological processes.
The inference of gene covariation networks from observational data can be
challenging, especially considering the large number of players involved and
the small number of biological replicates available for analysis. We propose a
new statistical method for estimating the number of erroneous edges in
reconstructed networks that strongly enhances commonly used inference
approaches. This method is based on a special relationship between sign of
correlation (positive/negative) and directionality (up/down) of gene
regulation, and allows for the identification and removal of approximately half
of all erroneous edges. Using the mathematical model of Bayesian networks and
positive correlation inequalities we establish a mathematical foundation for
our method. Analyzing existing biological datasets, we find a strong
correlation between the results of our method and false discovery rate (FDR).
Furthermore, simulation analysis demonstrates that our method provides a more
accurate estimate of network error than FDR.
Affine HJM Framework on $S_{d}^{+}$ and Long-Term Yield
Date: 2015-08-21 00:00:00

We develop the HJM framework for forward rates driven by affine processes on
the state space of symmetric positive matrices. In this setting we find a
representation for the long-term yield and investigate the yield's asymptotic
behaviour.
Varadhan's formula, conditioned diffusions, and local volatilities
Date: 2016-06-14 00:00:00

Motivated by marginals-mimicking results for It\^o processes via SDEs and by
their applications to volatility modeling in finance, we discuss the weak
convergence of the law of a hypoelliptic diffusions conditioned to belong to a
target affine subspace at final time, namely $\mathcal{L}(Z_t|Y_t = y)$ if
$X_{\cdot}=(Y_\cdot,Z_{\cdot})$. To do so, we revisit Varadhan-type estimates
in a small-noise regime (as opposed to small-time), studying the density of the
lower-dimensional component $Y$. The application to stochastic volatility
models include the small-time and, for certain models, the large-strike
asymptotics of the Gyongy-Dupire's local volatility function. The final product
are asymptotic formulae that can (i) motivate parameterizations of the local
volatility surface and (ii) be used to extrapolate local volatilities in a
given model.