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One approach to the analysis of stochastic fluctuations in market prices is to model characteristics of investor behaviour and the complex interactions between market participants, with the aim of extracting consequences in the aggregate.…
The accurate prediction of time-changing covariances is an important problem in the modeling of multivariate financial data. However, some of the most popular models suffer from a) overfitting problems and multiple local optima, b) failure…
The main objective of this paper is to develop a martingale-type solution to optimal consumption--investment choice problems ([Merton, 1969] and [Merton, 1971]) under time-varying incomplete preferences driven by externalities such as…
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from…
We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method for the optimal filter infinite dimensional Stochastic…
This paper gives a brief overview on the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inferences of instantaneous returns and volatility functions of time-homogeneous and…
The aim of this paper is to propose a new methodology that allows forecasting, through Vasicek and CIR models, of future expected interest rates (for each maturity) based on rolling windows from observed financial market data. The novelty,…
Non-equilibrium phenomena occur not only in physical world, but also in finance. In this work, stochastic relaxational dynamics (together with path integrals) is applied to option pricing theory. A recently proposed model (by Ilinski et…
In this paper, we investigate a portfolio selection problem with transaction costs under a two-factor stochastic volatility structure, where volatility follows a mean-reverting process with a stochastic mean-reversion level. The model…
The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…
The paper models foreign capital inflow from the developed to the developing countries in a stochastic dynamic programming (SDP) framework. Under some regularity conditions, the existence of the solutions to the SDP problem is proved and…
We show the application of an optimal transportation approach to estimate stochastic volatility process by using the flow that optimally transports the set of particles from the prior to a posterior distribution. We also show how to direct…
Forecasting time series on graphs is a fundamental problem in graph signal processing. When each entity of the network carries a vector of values for each time stamp instead of a scalar one, existing approaches resort to the use of product…
In this paper we introduce a projection method for the space of probability distributions based on the differential geometric approach to statistics. This method is based on a direct L2 metric as opposed to the usual Hellinger distance and…
This paper is concerned with particle filtering for $\alpha$-stable stochastic volatility models. The $\alpha$-stable distribution provides a flexible framework for modeling asymmetry and heavy tails, which is useful when modeling financial…
A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to…
Correlations between asset returns are important in many financial applications. In recent years, multivariate volatility models have been used to describe the time-varying feature of the correlations. However, the curse of dimensionality…
We study empirical covariance matrices in finance. Due to the limited amount of available input information, these objects incorporate a huge amount of noise, so their naive use in optimization procedures, such as portfolio selection, may…
The distributed filtering problem sequentially estimates a global state variable using observations from a network of local sensors with different measurement models. In this work, we introduce a novel methodology for distributed nonlinear…
This work is devoted to the study of modeling geophysical and financial time series. A class of volatility models with time-varying parameters is presented to forecast the volatility of time series in a stationary environment. The modeling…