669 research outputs found
Optimal phenotypic plasticity in a stochastic environment minimizes the cost/benefit ratio
This paper addresses the question of optimal phenotypic plasticity as a
response to environmental fluctuations while optimizing the cost/benefit ratio,
where the cost is energetic expense of plasticity, and benefit is fitness. The
dispersion matrix \Sigma of the genes' response (H = ln|\Sigma|) is used: (i)
in a numerical model as a metric of the phenotypic variance reduction in the
course of fitness optimization, then (ii) in an analytical model, in order to
optimize parameters under the constraint of limited energy availability.
Results lead to speculate that such optimized organisms should maximize their
exergy and thus the direct/indirect work they exert on the habitat. It is shown
that the optimal cost/benefit ratio belongs to an interval in which differences
between individuals should not substantially modify their fitness.
Consequently, even in the case of an ideal population, close to the optimal
plasticity, a certain level of genetic diversity should be long conserved, and
a part, still to be determined, of intra-populations genetic diversity probably
stem from environment fluctuations. Species confronted to monotonous factors
should be less plastic than vicariant species experiencing heterogeneous
environments. Analogies with the MaxEnt algorithm of E.T. Jaynes (1957) are
discussed, leading to the conjecture that this method may be applied even in
case of multivariate but non multinormal distributions of the responses
Modelling fluctuations of financial time series: from cascade process to stochastic volatility model
In this paper, we provide a simple, ``generic'' interpretation of
multifractal scaling laws and multiplicative cascade process paradigms in terms
of volatility correlations. We show that in this context 1/f power spectra, as
observed recently by Bonanno et al., naturally emerge. We then propose a simple
solvable ``stochastic volatility'' model for return fluctuations. This model is
able to reproduce most of recent empirical findings concerning financial time
series: no correlation between price variations, long-range volatility
correlations and multifractal statistics. Moreover, its extension to a
multivariate context, in order to model portfolio behavior, is very natural.
Comparisons to real data and other models proposed elsewhere are provided.Comment: 21 pages, 5 figure
Causal cascade in the stock market from the ``infrared'' to the ``ultraviolet''
Modelling accurately financial price variations is an essential step
underlying portfolio allocation optimization, derivative pricing and hedging,
fund management and trading. The observed complex price fluctuations guide and
constraint our theoretical understanding of agent interactions and of the
organization of the market. The gaussian paradigm of independent normally
distributed price increments has long been known to be incorrect with many
attempts to improve it. Econometric nonlinear autoregressive models with
conditional heteroskedasticity (ARCH) and their generalizations capture only
imperfectly the volatility correlations and the fat tails of the probability
distribution function (pdf) of price variations. Moreover, as far as changes in
time scales are concerned, the so-called ``aggregation'' properties of these
models are not easy to control. More recently, the leptokurticity of the full
pdf was described by a truncated ``additive'' L\'evy flight model (TLF).
Alternatively, Ghashghaie et al. proposed an analogy between price dynamics and
hydrodynamic turbulence. In this letter, we use wavelets to decompose the
volatility of intraday (S&P500) return data across scales. We show that when
investigating two-points correlation functions of the volatility logarithms
across different time scales, one reveals the existence of a causal information
cascade from large scales (i.e. small frequencies, hence to vocable
``infrared'') to fine scales (``ultraviolet''). We quantify and visualize the
information flux across scales. We provide a possible interpretation of our
findings in terms of market dynamics.Comment: 9 pages, 3 figure
A multivariate multifractal model for return fluctuations
In this paper we briefly review the recently inrtroduced Multifractal Random
Walk (MRW) that is able to reproduce most of recent empirical findings
concerning financial time-series : no correlation between price variations,
long-range volatility correlations and multifractal statistics. We then focus
on its extension to a multivariate context in order to model portfolio
behavior. Empirical estimations on real data suggest that this approach can be
pertinent to account for the nature of both linear and non-linear correlation
between stock returns at all time scales.Comment: To be published in the Proceeding of the APFA2 conference (Liege,
Belgium, July 2000) in the journal Quantitative Financ
Volatility fingerprints of large shocks: Endogeneous versus exogeneous
Finance is about how the continuous stream of news gets incorporated into
prices. But not all news have the same impact. Can one distinguish the effects
of the Sept. 11, 2001 attack or of the coup against Gorbachev on Aug., 19, 1991
from financial crashes such as Oct. 1987 as well as smaller volatility bursts?
Using a parsimonious autoregressive process with long-range memory defined on
the logarithm of the volatility, we predict strikingly different response
functions of the price volatility to great external shocks compared to what we
term endogeneous shocks, i.e., which result from the cooperative accumulation
of many small shocks. These predictions are remarkably well-confirmed
empirically on a hierarchy of volatility shocks. Our theory allows us to
classify two classes of events (endogeneous and exogeneous) with specific
signatures and characteristic precursors for the endogeneous class. It also
explains the origin of endogeneous shocks as the coherent accumulations of tiny
bad news, and thus unify all previous explanations of large crashes including
Oct. 1987.Comment: Latex document, 12 pages, 2 figure
Linear processes in high-dimension: phase space and critical properties
In this work we investigate the generic properties of a stochastic linear
model in the regime of high-dimensionality. We consider in particular the
Vector AutoRegressive model (VAR) and the multivariate Hawkes process. We
analyze both deterministic and random versions of these models, showing the
existence of a stable and an unstable phase. We find that along the transition
region separating the two regimes, the correlations of the process decay
slowly, and we characterize the conditions under which these slow correlations
are expected to become power-laws. We check our findings with numerical
simulations showing remarkable agreement with our predictions. We finally argue
that real systems with a strong degree of self-interaction are naturally
characterized by this type of slow relaxation of the correlations.Comment: 40 pages, 5 figure
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