Related papers: On three filtering problems arising in mathematica…
This note reviews our mathematical models for fish schooling, considered in free space, and in space with obstacle and food resource. These models are performed by stochastic differential equations or stochastic partial differential…
Kalman Filtering problems often have inherent and known constraints in the physical dynamics that are not exploited despite potentially significant gains (e.g., fixed speed of a motor). In this paper, we review existing methods and propose…
We study the emergence of instabilities in a stylized model of a financial market, when different market actors calculate prices according to different (local) market measures. We derive typical properties for ensembles of large random…
Local stochastic volatility refers to a popular model class in applied mathematical finance that allows for "calibration-on-the-fly", typically via a particle method, derived from a formal McKean-Vlasov equation. Well-posedness of this…
The 3DVAR filter is prototypical of methods used to combine observed data with a dynamical system, online, in order to improve estimation of the state of the system. Such methods are used for high dimensional data assimilation problems,…
Volatility, as a primary indicator of financial risk, forms the foundation of classical frameworks such as Markowitz's Portfolio Theory and the Efficient Market Hypothesis (EMH). However, its conventional use rests on assumptions-most…
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…
We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for…
This article studies convex duality in stochastic optimization over finite discrete-time. The first part of the paper gives general conditions that yield explicit expressions for the dual objective in many applications in operations…
Numerous kinds of uncertainties may affect an economy, e.g. economic, political, and environmental ones. We model the aggregate impact by the uncertainties on an economy and its associated financial market by randomised mixtures of L\'evy…
When a strict local martingale is projected onto a subfiltration to which it is not adapted, the local martingale property may be lost, and the finite variation part of the projection may have singular paths. This phenomenon has…
We consider a large market model of defaultable assets in which the asset price processes are modelled as Heston-type stochastic volatility models with default upon hitting a lower boundary. We assume that both the asset prices and their…
Numerous empirical proofs indicate the adequacy of the time discrete auto-regressive stochastic volatility models introduced by Taylor in the description of the log-returns of financial assets. The pricing and hedging of contingent products…
We forecast the full conditional distribution of macroeconomic outcomes by systematically integrating three key principles: using high-dimensional data with appropriate regularization, adopting rigorous out-of-sample validation procedures,…
This paper considers variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions and provides three stochastic approximation schemes to solve them. All methods use an empirical estimate of the CVaR…
We consider the problem of designing efficient particle filters for twisted Feynman--Kac models. Particle filters using twisted models can deliver low error approximations of statistical quantities and such twisting functions can be learnt…
The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the…
We investigate a new sampling scheme aimed at improving the performance of particle filters whenever (a) there is a significant mismatch between the assumed model dynamics and the actual system, or (b) the posterior probability tends to…
We consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on…
The aim of this work is to build financial crisis indicators based on spectral properties of the dynamics of market data. After choosing an optimal size for a rolling window, the historical market data in this window is seen every trading…