Related papers: Affine processes under parameter uncertainty
In this paper, we study the pricing of contracts in fixed income markets under volatility uncertainty in the sense of Knightian uncertainty or model uncertainty. The starting point is an arbitrage-free bond market under volatility…
We study an extension of the Cox-Ingersoll-Ross (CIR) process that incorporates jumps at deterministic dates, referred to as stochastic discontinuities. Our main motivation stems from short-rate modelling in the context of overnight rates,…
A mathematical framework for Continuous Time Finance based on operator algebraic methods offers a new direct and entirely constructive perspective on the field and leads to new numerical analysis techniques. This is partly a review paper as…
We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…
This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…
Model-based process design and operation involves here-and-now and wait-and-see decisions. Here-and-now decisions include design variables like the size of heat exchangers or the height of distillation columns, whereas wait-and-see…
We propose to model multivariate volatility processes based on the newly defined conditionally uncorrelated components (CUCs). This model represents a parsimonious representation for matrix-valued processes. It is flexible in the sense that…
We consider the covariance steering problem for nonlinear control-affine systems. Our objective is to find an optimal control strategy to steer the state of a system from an initial distribution to a target one whose mean and covariance are…
If an experimentalist observes a sequence of emitted quantum states via either projective or positive-operator-valued measurements, the outcomes form a time series. Individual time series are realizations of a stochastic process over the…
Experimental designs based on the classical D-optimal criterion minimize the volume of the linear-approximation inference regions for the parameters using local sensitivity coefficients. For nonlinear models, these designs can be unreliable…
We consider a stochastically continuous, affine Markov process in the sense of Duffie, Filipovic and Schachermayer, with cadlag paths, on a general state space D, i.e. an arbitrary Borel subset of R^d. We show that such a process is always…
Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e. robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management.…
For linear time-invariant systems with uncertain parameters belonging to a finite set, we present a purely deterministic approach to multiple-model estimation and propose an algorithm based on the minimax criterion using constrained…
Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error…
This paper deals with the identification of piecewise affine state-space models. These models are obtained by partitioning the state or input domain into a finite number of regions and by considering affine submodels in each region. The…
The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all…
It is known that, in general, an affine or Gabor AP-frame is an $L^2(\mathbb{R})$-frame and conversely. In part as a consequence of the Ergodic Theorem, we prove a necessary and sufficient condition for an affine (wavelet) system…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…