1,721,093 research outputs found
Anomalous behaviour of the correction to the central limit theorem for a model of random walk in random media.
No full textThe author considers a discrete-time random walk {X t } t=0 ∞ on Z ν for small dimension ν=1,2 with transition probabilities
P(X t+1 =y∣X t =x,ξ)=P 0 (y-x)+εc(y-x,ξ t (x)),
where ξ={ξ t (x), t=0,1,⋯, x∈Z ν } is a random environment such that the variables ξ t (x) are i.i.d., take values in a finite set and are such that 〈c(u,·)=0〉=0, where 〈·〉 denotes average with respect to the environment. ε is a small parameter.
The author shows that if is small enough and f is a smooth function, then as T→∞ the quantity
T lnT∑ x∈Z 2 [P(X T =x∣X 0 =0,ξ)-P 0 T (x)]fx-bT T
where b is the drift of the averaged random walk P 0 , tends in distribution to a gaussian random variable with covariance given by a suitable functional of f. Further results are proved for the random correction to the mean value and the covariance in dimension ν=1,2
A discrete trinomial model for the birth and death of stock financial bubbles
Full text linkThe present work proposes a novel way to model the dynamic of financial bubbles. In particular we exploit the so called trinomial tree technique, which is mainly inspired by the typical market order book (MOB) structure. According to the typical MOB rules, we exploit a bottom-up approach to derive the relevant generator process for the financial quantities characterizing the market we are considering. Our proposal pays attention in considering the real world changes in probability levels characterizing the bid-ask preferences, focusing the attention on the market movements. In particular, we show that financial bubbles are originated by these movements which also act amplify their growth
Autoregressive approaches to import–export time series II: a concrete case study
Full text linkThe present work constitutes the second part of a two-paper project that, in par-ticular, deals with an in-depth study of effective techniques used in econometrics in order tomake accurate forecasts in the concrete framework of one of the major economies of the mostproductive Italian area, namely the province of Verona. It is worth mentioning that this regionis indubitably recognized as the core of the commercial engine of the whole Italian country.This is why our analysis has a concrete impact; it is based on real data, and this is also thereason why particular attention has been taken in treating the relevant economical data and inchoosing the right methods to manage them to obtain good forecasts. In particular, we developan approach mainly based on vector autoregression where lagged values of two or more vari-ables are considered, Granger causality, and the stochastic trend approach useful to work withthe cointegration phenomenon
BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATION APPROACH TO STOCHASTIC DIFFERENTIAL UTILITY
Full text linkIn the present paper we find the solution for the stochastic differentialutility problem introduced by [2] using a backward stochastic Volterra integral differentialapproach. In particular we generalize results already obtained in literaturepassing from global to local Lipschitz assumption for the drift component
Autoregressive approaches to import–export time series I: basic techniques
Full text linkThis work is the first part of a project dealing with an in-depth study of effectivetechniques used in econometrics in order to make accurate forecasts in the concrete frameworkof one of the major economies of the most productive Italian area, namely the province ofVerona. In particular, we develop an approach mainly based on vector autoregressions, wherelagged values of two or more variables are considered, Granger causality, and the stochastictrend approach useful to work with the cointegration phenomenon. Latter techniques constitutethe core of the present paper, whereas in the second part of the project, we present how theseapproaches can be applied to economic data at our disposal in order to obtain concrete analysisof import–export behavior for the considered productive area of Verona
Maximal irreducibility measure for spatial birth-and-death processes
No full textWe prove that a spatial birth-and-death process is both φφ-irreducible and ψψ-irreducible under rather general conditions on the birth and death rates. It is also shown that every maximal irreducibility measure is equivalent to the Lebesgue-Poisson measure on the space of finite configuration
Backward Stochastic Differential Equations driven by Lévy noise with applications in Finance
No full textWe treat financial mathematical models driven
by noise of Lévy type in the framework of the backward stochastic
differential equations (BSDEs) theory. We shall present techniques
and results which are relevant from a mathematical point of views as
well in concrete market applications, since they allow to overcome the
discrepancies between real world financial data and classical models
which are based on Brownian diffusions.
BSEDs' techniques in presence of Lévy perturbations actually play
a major role in the solution of hedging and pricing problems especially
with respect to non-linear scenarios and for incomplete markets.
In particular, we provide an analogue of the celebrated Black-
Scholes formula, but the Lévy market case, with a clear economical
interpretation for all the involved ?nancial parameters, as well as an
introduction to the emerging ?eld of dynamic risk measures, for Lévy
driven BSDEs, making use of the concept of g − expectation in
presence of a Lipschitz driver
OPTIMAL EXECUTION STRATEGY UNDER ARITHMETIC BROWNIAN MOTION WITH VAR AND ES AS RISK PARAMETERS
Full text linkAbstract. We explicitly give the optimal trade execution strategy in the Almgren-Chriss framework, see [1,2], when the publicly available price process follows an arithmetic Brownian motion with zero drift. The financial setting is completed by choosing the risk parameters to be the Value at Risk and the Expected Shortfall associated with the Profit and Loss distribution of the strategy's position
Default Contagion in Financial Networks
Full text linkThe preset work aims at giving insights about howthe theory behind the study of complex networks can be profitablyused to analyse the increasing complexity characterizinga wide number of current financial frameworks. In particularwe exploit some well known approaches developed within thesetting of the graph theory, such as, e.g., the Erd ̋os and Rénymodel, and the Barab ́asi-Albert model, as well as producingan analysis based on the evolving network theory. Numericalsimulations are performed to study the spread of financial peakevents, as in the case of the default of a single bank belonging toa net of interconnected monetary institutions, showing how theknowledge about the underlying graph theory can be effectivelyused to withstand a financial default contagion
A maximum principle for a stochastic control problem with multiple random terminal times
Full text linkIn the present paper we derive, via a backward induction technique, an ad hoc maximum principle for an optimal control problem with multiple random terminal times. We thus apply the aforementioned result to the case of a linear quadratic controller, providing solutions for the optimal control in terms of Riccati backward SDE with random terminal time
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