pwc-archive/papers-with-abstracts huggingface dataset:
Large Portfolio Asymptotics for Loss From Default
Date: 2015-02-18 00:00:00

We prove a law of large numbers for the loss from default and use it for
approximating the distribution of the loss from default in large, potentially
heterogenous portfolios. The density of the limiting measure is shown to solve
a non-linear SPDE, and the moments of the limiting measure are shown to satisfy
an infinite system of SDEs. The solution to this system leads to %the solution
to the SPDE through an inverse moment problem, and to the distribution of the
limiting portfolio loss, which we propose as an approximation to the loss
distribution for a large portfolio. Numerical tests illustrate the accuracy of
the approximation, and highlight its computational advantages over a direct
Monte Carlo simulation of the original stochastic system.
Stability of nonconstant stationary solutions in a reaction-diffusion equation coupled to the system of ordinary differential equations
Date: 2016-04-23 00:00:00

In this paper we study pattern formation arising in a system of a single
reaction-diffusion equation coupled with subsystem of ordinary differential
equations, describing spatially-distributed growth of clonal populations of
precancerous cells, whose proliferation is controled by growth factors
diffusing in the extracellular medium and binding to the cell surface. We
extend the results on the existence of nonhomogenous stationary solutions
obtained in the previous work of one of the authors to a general Hill-type
production function and full parameter set. Using spectral analysis and
perturbation theory we derive conditions for the linearized stability of such
spatial patterns.
A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk
Date: 2015-09-21 00:00:00

This paper considers exponential utility indifference pricing for a
multidimensional non-traded assets model subject to inter-temporal default
risk, and provides a semigroup approximation for the utility indifference
price. The key tool is the splitting method, whose convergence is proved based
on the Barles-Souganidis monotone scheme, and the convergence rate is derived
based on Krylov's shaking the coefficients technique. We apply our methodology
to study the counterparty risk of derivatives in incomplete markets.
Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction
Date: 2016-09-14 00:00:00

Cellular signal transduction usually involves activation cascades, the
sequential activation of a series of proteins following the reception of an
input signal. Here we study the classic model of weakly activated cascades and
obtain analytical solutions for a variety of inputs. We show that in the
special but important case of optimal-gain cascades (i.e., when the
deactivation rates are identical) the downstream output of the cascade can be
represented exactly as a lumped nonlinear module containing an incomplete gamma
function with real parameters that depend on the rates and length of the
cascade, as well as parameters of the input signal. The expressions obtained
can be applied to the non-identical case when the deactivation rates are random
to capture the variability in the cascade outputs. We also show that cascades
can be rearranged so that blocks with similar rates can be lumped and
represented through our nonlinear modules. Our results can be used both to
represent cascades in computational models of differential equations and to fit
data efficiently, by reducing the number of equations and parameters involved.
In particular, the length of the cascade appears as a real-valued parameter and
can thus be fitted in the same manner as Hill coefficients. Finally, we show
how the obtained nonlinear modules can be used instead of delay differential
equations to model delays in signal transduction.
Utility maximization with addictive consumption habit formation in incomplete semimartingale markets
Date: 2015-05-28 00:00:00

This paper studies the continuous time utility maximization problem on
consumption with addictive habit formation in incomplete semimartingale
markets. Introducing the set of auxiliary state processes and the modified dual
space, we embed our original problem into a time-separable utility maximization
problem with a shadow random endowment on the product space
$\mathbb{L}_+^0(\Omega\times [0,T],\mathcal{O},\overline{\mathbb{P}})$.
Existence and uniqueness of the optimal solution are established using convex
duality approach, where the primal value function is defined on two variables,
that is, the initial wealth and the initial standard of living. We also provide
sufficient conditions on the stochastic discounting processes and on the
utility function for the well-posedness of the original optimization problem.
Under the same assumptions, classical proofs in the approach of convex duality
analysis can be modified when the auxiliary dual process is not necessarily
integrable.
A CDS Option Miscellany
Authors: Richard J Martin
Date: 2011-12-30 00:00:00

CDS options allow investors to express a view on spread volatility and obtain a wider range of payoffs than are possible with vanilla CDS. We give a detailed exposition of different types of single-name CDS option, including options with upfront protection payment, recovery options and recovery swaps, and also presents a new formula for the index option. The emphasis is on using the Black-76 formula where possible and ensuring consistency within asset classes. In the framework shown here the `armageddon event' does not require special attention.
Infinite graphs in systematic biology, with an application to the species problem
Date: 2019-11-16 00:00:00

We argue that C. Darwin and more recently W. Hennig worked at times under the
simplifying assumption of an eternal biosphere. So motivated, we explicitly
consider the consequences which follow mathematically from this assumption, and
the infinite graphs it leads to. This assumption admits certain clusters of
organisms which have some ideal theoretical properties of species, shining some
light onto the species problem. We prove a dualization of a law of T.A. Knight
and C. Darwin, and sketch a decomposition result involving the internodons of
D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond
to B. Sturmfels' question, "Can biology lead to new theorems?"
Health Matters: Human Organ Donations, Sales, and the Black Market
Date: 2015-01-13 00:00:00

In this paper I explore the human organ procurement system. Which is better
for saving lives and limiting black market use, the present altruistic system
of donations or a free and open sales market? I explain that there is a risk
with maintaining the present system, the altruistic vision, and that people may
die who might otherwise live if the sale of organs was permitted. But there is
no guarantee that permitting organ sales would effectively address the current
supply-side shortage and global use of the black market. In addition to
discussing the implications of these procurement systems, I look at methods to
increase organ donations and I explore the differences between presumed and
explicit consent. Ultimately, I conclude that the altruistic donation system,
bolstered by the addition of a policy of presumed consent and appropriate
financial incentives, is a better choice than a legal sales market in spite of
its shortcomings.
Max-Sum Diversification, Monotone Submodular Functions and Dynamic Updates
Authors: Borodin Allan, Jain Aadhar, Lee Hyun Chul, Ye Yuli
Date: 2016-11-25 00:00:00
Tasks: Document Summarization, Management

Result diversification is an important aspect in web-based search, document
summarization, facility location, portfolio management and other applications.
Given a set of ranked results for a set of objects (e.g. web documents,
facilities, etc.) with a distance between any pair, the goal is to select a
subset $S$ satisfying the following three criteria: (a) the subset $S$
satisfies some constraint (e.g. bounded cardinality); (b) the subset contains
results of high "quality"; and (c) the subset contains results that are
"diverse" relative to the distance measure. The goal of result diversification
is to produce a diversified subset while maintaining high quality as much as
possible. We study a broad class of problems where the distances are a metric,
where the constraint is given by independence in a matroid, where quality is
determined by a monotone submodular function, and diversity is defined as the
sum of distances between objects in $S$. Our problem is a generalization of the
{\em max sum diversification} problem studied in \cite{GoSh09} which in turn is
a generaliztion of the {\em max sum $p$-dispersion problem} studied extensively
in location theory. It is NP-hard even with the triangle inequality. We propose
two simple and natural algorithms: a greedy algorithm for a cardinality
constraint and a local search algorithm for an arbitary matroid constraint. We
prove that both algorithms achieve constant approximation ratios.
The Effect of Market Power on Risk-Sharing
Date: 2016-05-17 00:00:00

The paper studies an oligopolistic equilibrium model of financial agents who
aim to share their random endowments. The risk-sharing securities and their
prices are endogenously determined as the outcome of a strategic game played
among all the participating agents. In the complete-market setting, each
agent's set of strategic choices consists of the security payoffs and the
pricing kernel that are consistent with the optimal-sharing rules; while in the
incomplete setting, agents respond via demand functions on a vector of given
tradeable securities. It is shown that at the (Nash) risk-sharing equilibrium,
the sharing securities are suboptimal, since agents submit for sharing
different risk exposures than their true endowments. On the other hand, the
Nash equilibrium prices stay unaffected by the game only in the special case of
agents with the same risk aversion. In addition, agents with sufficiently lower
risk aversion act as predatory traders, since they absorb utility surplus from
the high risk averse agents and reduce the efficiency of sharing. The main
results of the paper also hold under the generalized models that allow the
presence of noise traders and heterogeneity in agents' beliefs.
Robust exponential binary pattern storage in Little-Hopfield networks
Date: 2015-04-29 00:00:00
Tasks: Denoising, Retrieval

The Little-Hopfield network is an auto-associative computational model of
neural memory storage and retrieval. This model is known to robustly store
collections of randomly generated binary patterns as stable-states of the
network dynamics. However, the number of binary memories so storable scales
linearly in the number of neurons, and it has been a long-standing open problem
whether robust exponential storage of binary patterns was possible in such a
network memory model. In this note, we design simple families of
Little-Hopfield networks that provably solve this problem affirmatively. As a
byproduct, we produce a set of novel (nonlinear) binary codes with an
efficient, highly parallelizable denoising mechanism.
Studying RNA homology and conservation with Infernal: from single sequences to RNA families
Date: 2016-01-26 00:00:00

Emerging high-throughput technologies have led to a deluge of putative
non-coding RNA (ncRNA) sequences identified in a wide variety of organisms.
Systematic characterization of these transcripts will be a tremendous
challenge. Homology detection is critical to making maximal use of functional
information gathered about ncRNAs: identifying homologous sequence allows us to
transfer information gathered in one organism to another quickly and with a
high degree of confidence. ncRNA presents a challenge for homology detection,
as the primary sequence is often poorly conserved and de novo secondary
structure prediction and search remains difficult. This protocol introduces
methods developed by the Rfam database for identifying "families" of homologous
ncRNAs starting from single "seed" sequences using manually curated sequence
alignments to build powerful statistical models of sequence and structure
conservation known as covariance models (CMs), implemented in the Infernal
software package. We provide a step-by-step iterative protocol for identifying
ncRNA homologs, then constructing an alignment and corresponding CM. We also
work through an example for the bacterial small RNA MicA, discovering a
previously unreported family of divergent MicA homologs in genus Xenorhabdus in
the process.
An Evolutionary Framework for Culture: Selectionism versus Communal Exchange
Date: 2019-06-30 00:00:00
Tasks: Cultural Vocal Bursts Intensity Prediction

Dawkins' replicator-based conception of evolution has led to widespread
mis-application selectionism across the social sciences because it does not
address the paradox that inspired the theory of natural selection in the first
place: how do organisms accumulate change when traits acquired over their
lifetime are obliterated? This is addressed by von Neumann's concept of a
self-replicating automaton (SRA). A SRA consists of a self-assembly code that
is used in two distinct ways: (1) actively deciphered during development to
construct a self-similar replicant, and (2) passively copied to the replicant
to ensure that it can reproduce. Information that is acquired over a lifetime
is not transmitted to offspring, whereas information that is inherited during
copying is transmitted. In cultural evolution there is no mechanism for
discarding acquired change. Acquired change can accumulate orders of magnitude
faster than, and quickly overwhelm, inherited change due to differential
replication of variants in response to selection. This prohibits a selectionist
but not an evolutionary framework for culture. Recent work on the origin of
life suggests that early life evolved through a non-Darwinian process referred
to as communal exchange that does not involve a self-assembly code, and that
natural selection emerged from this more haphazard, ancestral evolutionary
process. It is proposed that communal exchange provides a more appropriate
evolutionary framework for culture than selectionism. This is supported by a
computational model of cultural evolution and a network-based program for
documenting material cultural history, and it is consistent with high levels of
human cooperation.
A Test of the Adaptive Market Hypothesis using a Time-Varying AR Model in Japan
Date: 2016-01-21 00:00:00

This study examines the adaptive market hypothesis (AMH) in Japanese stock
markets (TOPIX and TSE2). In particular, we measure the degree of market
efficiency by using a time-varying model approach. The empirical results show
that (1) the degree of market efficiency changes over time in the two markets,
(2) the level of market efficiency of the TSE2 is lower than that of the TOPIX
in most periods, and (3) the market efficiency of the TOPIX has evolved, but
that of the TSE2 has not. We conclude that the results support the AMH for the
more qualified stock market in Japan.
Investor's sentiment in multi-agent model of the continuous double auction
Date: 2016-02-17 00:00:00
Tasks: Mathematical Proofs

We introduce and treat rigorously a new multi-agent model of the continuous
double auction or in other words the order book (OB). It is designed to explain
collective behaviour of the market when new information affecting the market
arrives. The novel feature of the model is two additional slow changing
parameters, the so-called sentiment functions. These sentiment functions
measure the conception of the fair price of two groups of investors, namely,
bulls and bears. Our model specifies differential equations for the time
evolution of sentiment functions and constitutes a nonlinear Markov process
which exhibits long term correlations. We explain the intuition behind
equations for sentiment functions and present numerical simulations which show
that the behaviour of our model is similar to the behaviour of the real market.
We also obtain a diffusion limit of the model, the Ornstein-Uhlenbeck type
process with variable volatility. The volatility is proportional to the
difference of opinions of bulls and bears about the fair price of a security.
The paper is complimentary to our previous work where mathematical proofs are
presented.
Reverse Engineering Gene Interaction Networks Using the Phi-Mixing Coefficient
Date: 2016-03-12 00:00:00

Constructing gene interaction networks (GINs) from high-throughput gene
expression data is an important and challenging problem in systems biology.
Existing algorithms produce networks that either have undirected and unweighted
edges, or else are constrained to contain no cycles, both of which are
biologically unrealistic. In the present paper we propose a new algorithm,
based on a concept from probability theory known as the phi-mixing coefficient,
that produces networks whose edges are weighted and directed, and are permitted
to contain cycles. Because there is no "ground truth" for genome-wide networks
on a human scale, we analyzed the outcomes of several experiments on lung
cancer, and matched the predictions from the inferred networks with
experimental results. Specifically, we inferred three networks (NSCLC,
Neuro-endocrine NSCLC plus SCLC, and normal) from the gene expression
measurements of 157 lung cancer and 59 normal cell lines, compared with the
outcomes of siRNA screening of 19,000+ genes on 11 NSCLC cell lines, and
analyzed data from a ChIP-Seq experiment to determine putative downstream
targets of the lineage specific oncogenic transcription factor ASCL1. The
inferred networks displayed a scale-free or power law behavior between the
degree of a node and the number of nodes with that degree. There was a strong
correlation between the degree of a gene in the inferred NSCLC network and its
essentiality for the survival of the cells. The inferred downstream
neighborhood genes of ASCL1 in the SCLC network were significantly enriched by
ChIP-Seq determined putative target genes, while no such enrichment was found
in the inferred NSCLC network.
Second Order Multiscale Stochastic Volatility Asymptotics: Stochastic Terminal Layer Analysis & Calibration
Date: 2015-09-16 00:00:00
Tasks: Portfolio Optimization

Multiscale stochastic volatility models have been developed as an efficient
way to capture the principle effects on derivative pricing and portfolio
optimization of randomly varying volatility. The recent book Fouque,
Papanicolaou, Sircar and S{\o}lna (2011, CUP) analyzes models in which the
volatility of the underlying is driven by two diffusions -- one fast
mean-reverting and one slow-varying, and provides a first order approximation
for European option prices and for the implied volatility surface, which is
calibrated to market data. Here, we present the full second order asymptotics,
which are considerably more complicated due to a terminal layer near the option
expiration time. We find that, to second order, the implied volatility
approximation depends quadratically on log-moneyness, capturing the convexity
of the implied volatility curve seen in data. We introduce a new probabilistic
approach to the terminal layer analysis needed for the derivation of the second
order singular perturbation term, and calibrate to S&P 500 options data.
Funding Liquidity, Debt Tenor Structure, and Creditor's Belief: An Exogenous Dynamic Debt Run Model
Date: 2015-03-31 00:00:00

We propose a unified structural credit risk model incorporating both
insolvency and illiquidity risks, in order to investigate how a firm's default
probability depends on the liquidity risk associated with its financing
structure. We assume the firm finances its risky assets by mainly issuing
short- and long-term debt. Short-term debt can have either a discrete or a more
realistic staggered tenor structure. At rollover dates of short-term debt,
creditors face a dynamic coordination problem. We show that a unique threshold
strategy (i.e., a debt run barrier) exists for short-term creditors to decide
when to withdraw their funding, and this strategy is closely related to the
solution of a non-standard optimal stopping time problem with control
constraints. We decompose the total credit risk into an insolvency component
and an illiquidity component based on such an endogenous debt run barrier
together with an exogenous insolvency barrier.
Sequential $\delta$-optimal consumption and investment for stochastic volatility markets with unknown parameters
Date: 2015-05-14 00:00:00

We consider an optimal investment and consumption problem for a Black-Scholes
financial market with stochastic volatility and unknown stock appreciation
rate. The volatility parameter is driven by an external economic factor modeled
as a diffusion process of Ornstein-Uhlenbeck type with unknown drift. We use
the dynamical programming approach and find an optimal financial strategy which
depends on the drift parameter. To estimate the drift coefficient we observe
the economic factor $Y$ in an interval $[0,T_0]$ for fixed $T_0>0$, and use
sequential estimation. We show, that the consumption and investment strategy
calculated through this sequential procedure is $\delta$-optimal.
Valuation of asset and volatility derivatives using decoupled time-changed L\'evy processes
Date: 2015-01-31 00:00:00

In this paper we propose a general derivative pricing framework which employs
decoupled time-changed (DTC) L\'evy processes to model the underlying asset of
contingent claims. A DTC L\'evy process is a generalized time-changed L\'evy
process whose continuous and pure jump parts are allowed to follow separate
random time scalings; we devise the martingale structure for a DTC
L\'evy-driven asset and revisit many popular models which fall under this
framework. Postulating different time changes for the underlying L\'evy
decomposition allows to introduce asset price models consistent with the
assumption of a correlated pair of continuous and jump market activities; we
study one illustrative DTC model having this property by assuming that the
instantaneous activity rates follow the the so-called Wishart process. The
theory developed is applied to the problem of pricing claims depending not only
on the price or the volatility of an underlying asset, but also to more
sophisticated derivatives that pay-off on the joint performance of these two
financial variables, like the target volatility option (TVO). We solve the
pricing problem through a Fourier-inversion method; numerical computations
validating our technique are provided.
Generalised arbitrage-free SVI volatility surfaces
Date: 2016-05-27 00:00:00

In this article we propose a generalisation of the recent work of Gatheral
and Jacquier on explicit arbitrage-free parameterisations of implied volatility
surfaces. We also discuss extensively the notion of arbitrage freeness and
Roger Lee's moment formula using the recent analysis by Roper. We further
exhibit an arbitrage-free volatility surface different from Gatheral's SVI
parameterisation.