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188
Characterizations of joint distributions, copulas, information, dependence and decoupling, with applications to time series
 IMS LECTURE NOTES–MONOGRAPH SERIES
, 2006
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Artificial Financial Markets: An Agent Based . . .
, 2007
"... Stock markets are very important in modern societies and their behaviour have serious implications in a wide spectrum of the world’s population. Investors, governing bodies and the society as a whole could benefit from better understanding of the behaviour of stock markets. The traditional approach ..."
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Stock markets are very important in modern societies and their behaviour have serious implications in a wide spectrum of the world’s population. Investors, governing bodies and the society as a whole could benefit from better understanding of the behaviour of stock markets. The traditional approach to analyze such systems is the use of analytical models. However, the complexity of financial markets represents a big challenge to the analytical approach. Most analytical models make simplifying assumptions, such as perfect rationality and homogeneous investors, which threaten the validity of analytical results. This motivates the use of alternative methods. For those reasons, the study of such markets is a fertile field to use the agentbased methodology. In this work, we developed an artificial financial market and used it to study the behaviour of stock markets. In this market, we model technical, fundamental and noise traders. The technical traders are nonsimple genetic programming based agents that coevolve (by means of their fitness function) by predicting investment opportunities in the market using technical analysis as the main tool. Such traders are equipped with
FORECASTING VOLATILITY WITH THE MULTIFRACTAL RANDOM WALK MODEL
, 801
"... Abstract. We study the problem of forecasting volatility for the multifractal random walk model. In order to avoid the ill posed problem of estimating the correlation length T of the model, we introduce a limiting object defined in a quotient space; formally, this object is an infinite range logvola ..."
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Abstract. We study the problem of forecasting volatility for the multifractal random walk model. In order to avoid the ill posed problem of estimating the correlation length T of the model, we introduce a limiting object defined in a quotient space; formally, this object is an infinite range logvolatility. For this object and the non limiting object, we obtain precise prediction formulas and we apply them to the problem of forecasting volatility and pricing options with the MRW model in the absence of a reliable estimate of σ and T.
Minimal agent based model for financial markets II: statistical properties of the linear and multiplicative dynamics. to be submitted
, 2008
"... We introduce a minimal Agent Based Model for financial markets to understand the nature and SelfOrganization of the Stylized Facts. The model is minimal in the sense that we try to identify the essential ingredients to reproduce the main most important deviations of price time series from a Random ..."
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We introduce a minimal Agent Based Model for financial markets to understand the nature and SelfOrganization of the Stylized Facts. The model is minimal in the sense that we try to identify the essential ingredients to reproduce the main most important deviations of price time series from a Random Walk behavior. We focus on four essential ingredients: fundamentalist agents which tend to stabilize the market; chartist agents which induce destabilization; analysis of price behavior for the two strategies; herding behavior which governs the possibility of changing strategy. Bubbles and crashes correspond to situations dominated by chartists, while fundamentalists provide a long time stability (on average). The Stylized Facts are shown to correspond to an intermittent behavior which occurs only for a finite value of the number of agents N. Therefore they correspond to finite size effect which, however, can occur at different time scales. We propose a new mechanism for the SelfOrganization of this state which is linked to the existence of a threshold for the agents to be active or not active. The feedback between price fluctuations and number of active agents represent a crucial element for this state of SelfOrganizedIntermittency. The model can be easily generalized to consider more realistic variants. 1
Optimal algorithms for ksearch with applications in option pricing
 In ESA 2007, Proceedings 15th Annual European Symposium
, 2007
"... Abstract. In the ksearch problem, a player is searching for the k highest (respectively, lowest) prices in a sequence, which is revealed to her sequentially. At each quotation, the player has to decide immediately whether to accept the price or not. Using the competitive ratio as a performance meas ..."
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Abstract. In the ksearch problem, a player is searching for the k highest (respectively, lowest) prices in a sequence, which is revealed to her sequentially. At each quotation, the player has to decide immediately whether to accept the price or not. Using the competitive ratio as a performance measure, we give optimal deterministic and randomized algorithms for both the maximization and minimization problems, and discover that the problems behave substantially different in the worstcase. As an application of our results, we use these algorithms to price “lookback options”, a particular class of financial derivatives. We derive bounds for the price of these securities under a noarbitrage assumption, and compare this to classical option pricing. 1
Social Simulation of Stock Markets: Taking It to the Next Level
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An adaptive Markov Chain Monte Carlo method for GARCH model
, 2009
"... Abstract. We propose a method to construct a proposal density for the MetropolisHastings algorithm in Markov Chain Monte Carlo (MCMC) simulations of the GARCH model. The proposal density is constructed adaptively by using the data sampled by the MCMC method itself. It turns out that autocorrelation ..."
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Cited by 4 (4 self)
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Abstract. We propose a method to construct a proposal density for the MetropolisHastings algorithm in Markov Chain Monte Carlo (MCMC) simulations of the GARCH model. The proposal density is constructed adaptively by using the data sampled by the MCMC method itself. It turns out that autocorrelations between the data generated with our adaptive proposal density are greatly reduced. Thus it is concluded that the adaptive construction method is very efficient and works well for the MCMC simulations of the GARCH model.
GAUSSIAN MULTIPLICATIVE CHAOS REVISITED
, 807
"... Abstract. In this article, we extend the theory of multiplicative chaos for positive definite functions in Rd of the form f(x) = λ2 + T ln x + g(x) where g is a continuous and bounded function. The construction is simpler and more general than the one defined by Kahane in 1985. As main applicatio ..."
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Abstract. In this article, we extend the theory of multiplicative chaos for positive definite functions in Rd of the form f(x) = λ2 + T ln x + g(x) where g is a continuous and bounded function. The construction is simpler and more general than the one defined by Kahane in 1985. As main application, we give a rigorous mathematical meaning to the KolmogorovObukhov model of energy dissipation in a turbulent flow.