Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to finite state, continuous time Markov chains, we develop a theory of nonlinear expe…
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48 results for “dynamic nonlinear expectations”
We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so it is beyond the scope of Peng's framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic se…
We study the dynamic indifference pricing with ambiguity preferences. For this, we introduce the dynamic expected utility with ambiguity via the nonlinear expectation--G-expectation, introduced by Peng (2007). We also study the risk aversion and certainty equivalent for the agents with ambiguity. We obtain the dynamic …
We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a càdlàg nonlinear martingale which is also the value process of a superhedging problem. The superhedging strate…
This work examines the stability of GD and SGD near minima, revealing nonlinear dynamics that differ from linear analysis.
problem The stability of optimization algorithms like GD and SGD near minima is not well understood.
method The authors derive an exact criterion for stable oscillations of GD near minima in the multivariate setting, considering high-order derivatives.
result Nonlinear dynamics can diverge in expectation even if a single batch is unstable, challenging linear analysis.
Defines -expectation of distributions and its applications.
problem Defining -expectation of distributions.
method Two special cases of nonlinear and law-invariant -expectation.
result Explicit derivation of -expectation of distributions.
Controller seeks informative system observations to predict nonlinear dynamics.
problem Predicting nonlinear dynamics with uncertain parameters.
method Expected free energy minimization for balancing goal state and informative observations.
result Controller improves performance in uncertain parameter scenarios.
Breaks down complex nonlinear dynamics into simpler components.
problem Control of nonlinear dynamical systems remains challenging.
method Inspired by hybrid switching systems, decomposes dynamics into simpler stochastic switching linear dynamical systems.
result Extracts hierarchies of Markovian and auto-regressive locally linear controllers from nonlinear experts.
We study time consistent dynamic pricing mechanisms of European contingent claims under uncertainty by using G framework introduced by Peng ([24]). We consider a financial market consisting of a riskless asset and a risky stock with price process modelled by a geometric generalized G-Brownian motion, which features the…
Data-Efficient Non-Gaussian Semi-Nonparametric Density Estimation for Nonlinear Dynamical Systemsmath.OC
This paper presents a method for efficient density estimation in nonlinear systems.
problem Accurate representation of non-Gaussian distributions in nonlinear dynamical systems is challenging.
method Uses Seminonparametric (SNP) densities with probabilists' Hermite polynomial basis and Monte Carlo approximation for maximum likelihood estimation.
result Demonstrates that the method can accurately capture non-Gaussian density structure and compute quantiles using fewer samples than raw Monte Carlo.
We analyze an optimal stopping problem with random maturity under a nonlinear expectation with respect to a weakly compact set of mutually singular probabilities . The maturity is specified as the hitting time to level of some continuous index process at which the payoff process is even allowed to have…
The paper extends asset pricing theory by considering conditional markets.
problem Analyzing financial markets with conditional information.
method Time consistency properties of dynamic nonlinear expectations applied to super- and subhedging prices.
result Derives a conditional version of the second fundamental theorem of asset pricing.
Framework for reconstructing nonlinear systems from multi-modal time series data.
problem Reconstructing nonlinear dynamical systems from multi-modal time series data.
method Dynamic interpretable recurrent neural networks coupled with generalized linear models for multi-modal data integration.
result Framework efficiently compensates for noisy or missing information in one data channel using other channels.
This paper deals with multidimensional dynamic risk measures induced by conditional -expectations. A notion of multidimensional -expectation is proposed to provide a multidimensional version of nonlinear expectations. By a technical result on explicit expressions for the comparison theorem, uniqueness theorem and…
We consider a stochastic control problem for a class of nonlinear kernels. More precisely, our problem of interest consists in the optimisation, over a set of possibly non-dominated probability measures, of solutions of backward stochastic differential equations (BSDEs). Since BSDEs are nonlinear generalisations of the…
We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may be readily extended to nonlinear systems - with a reasonable expectation of suc…
New model combines ICA and HMM for unsupervised learning of nonstationary time series.
problem Manual segmentation of non-stationary data is computationally expensive and inaccurate.
method Combines Hidden Markov Model with nonlinear ICA for unsupervised learning.
result Proves identifiability of the model for general mixing nonlinearity.
DynNet models dynamic responses of linear and nonlinear systems with fewer variables and higher accuracy.
problem Predicting dynamic responses of linear and nonlinear systems.
method Physics-based recurrent neural network with optimized architecture and training techniques.
result Higher accuracy and fewer trainable variables compared to existing models.
This work uses a scalable approach to identify partially observed nonlinear systems.
problem Offline identification of partially observed nonlinear systems.
method Certainty-equivalent expectation-maximization (CEEM) as block coordinate-ascent.
result The CEEM approach can identify high-dimensional systems reliably and efficiently.
In this paper, we investigate risk minimization problem of derivatives based on non-tradable underlyings by means of dynamic g-expectations which are slight different from conditional g-expectations. In this framework, inspired by [1] and [16], we introduce risk indifference price, marginal risk price and derivative he…
New insights and algorithms improve prediction models with time-series privileged information.
problem Efficient learning of nonlinear prediction models with limited data.
method Generalization of LuPI to nonlinear tasks, using random features and representation learning.
result Theoretical and empirical evidence supports the use of privileged time-series information for nonlinear prediction.
Estimates hybrid dynamical systems with polynomial expansions and Markovian switching.
problem Identifying hybrid dynamical systems with nonlinear autoregressive exogenous (NARX) components and Markovian switching.
method Probabilistic framework using Expectation Maximization for parameter estimation, including submodel coefficients, hidden state values, and transition probabilities. Disentangles mode classification and NARX regression tasks. Uses soft-labels and coordinate descent approach for parameter fitting.
result Demonstrated on a SMNARX problem with three nonlinear sub-models, achieving parsimonious models through l1-norm bridge estimation and hard-thresholding.
Optimal investment with insurable background risk and nonlinear portfolio allocation frictionsq-fin.MF
Investment and insurance decisions are studied in a model with nonlinear portfolio frictions and background risk.
problem Investment and insurance decisions under a model with nonlinear portfolio frictions and background risk.
method Dynamic programming approach to find optimality conditions.
result Agent can choose to assume, partially assume, or purchase total insurance against adverse jumps in wealth.
We propose two rational expectation models of transient financial bubbles with heterogeneous arbitrageurs and positive feedbacks leading to self-reinforcing transient stochastic faster-than-exponential price dynamics. As a result of the nonlinear feedbacks, the termination of a bubble is found to be characterized by a …
In this paper, we propose a dynamical systems perspective of the Expectation-Maximization (EM) algorithm. More precisely, we can analyze the EM algorithm as a nonlinear state-space dynamical system. The EM algorithm is widely adopted for data clustering and density estimation in statistics, control systems, and machine…
While there are convergence guarantees for temporal difference (TD) learning when using linear function approximators, the situation for nonlinear models is far less understood, and divergent examples are known. Here we take a first step towards extending theoretical convergence guarantees to TD learning with nonlinear…
We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations with Lipschitz continuous …
A new method improves Bayesian filtering in nonlinear systems.
problem Bayesian filtering in nonlinear dynamical systems with non-Gaussian posteriors.
method Transport maps with block-triangular structure and gradient flows for MMD minimization.
result Accurate approximation of non-Gaussian posteriors without particle collapse.
Study optimal investment and consumption in incomplete markets with nonlinear expectations.
problem Utility maximization in incomplete markets with general constraints.
method Utilizes -martingale method to solve optimization problem for various utility functions.
result Characterizes optimal investment-consumption strategy through quadratic BSDE solutions.
Financial Resilience Evaluation: From Conditional Expectations to Dynamic Convex Risk Measuresq-fin.MF
Enhances resilience evaluation by using dynamic convex risk measures.
problem Capturing the full risk profile of financial positions under adverse conditions.
method Introduces a new resilience evaluation method using dynamic convex risk measures.
result Shows that the resilience evaluation can distinguish between positions with the same expected recovery but different conditional risk profiles.
Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions (which form a nonlinear space), equivalently, on random closed sets. …
The study analyzes the performance of a nonparametric estimator for dynamical systems.
problem Analyzing the performance of a nonparametric estimator for dynamical systems.
method Nonparametric least squares estimator (LSE) and information-theoretic methods.
result Rate-optimal error bounds for nonparametric hypotheses classes.
Viscosity properties with singularities in a state-constrained expected utility maximization problemq-fin.MF
We consider the value function originating from an expected utility maximization problem with finite fuel constraint and show its close relation to a nonlinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity. On one hand, we give a so-called verification argument based on the dynamic progr…
In this paper, we study a type of reflected BSDE with a constraint and introduce a new kind of nonlinear expectation via BSDE with a constraint and prove the Doob-Meyer decomposition with respect to the super(sub)martingale introduced by this nonlinear expectation. We then apply the results to the pricing of American o…
Keeping a basic tenet of economic theory, rational expectations, we model the nonlinear positive feedback between agents in the stock market as an interplay between nonlinearity and multiplicative noise. The derived hyperbolic stochastic finite-time singularity formula transforms a Gaussian white noise into a rich time…
AdaKoop efficiently models nonlinear dynamics from nonstationary data streams.
problem Capturing nonlinear dynamics in nonstationary data streams with computational efficiency.
method Koopman operator theory and probabilistic framework for streaming data.
result AdaKoop outperforms state-of-the-art methods in real-time forecasting accuracy and efficiency.
In this paper we investigate a dynamic stochastic portfolio optimization problem involving both the expected terminal utility and intertemporal utility maximization. We solve the problem by means of a solution to a fully nonlinear evolutionary Hamilton-Jacobi-Bellman (HJB) equation. We propose the so-called Riccati met…
The paper introduces a fast algorithm for learning and forecasting nonlinear dynamics from noisy time series data.
problem Challenges in capturing nonlinear dynamics from noisy time series data.
method A projected nonlinear state-space model with kernel functions applied to projected lines.
result The model effectively learns and forecasts complex nonlinear dynamics with computational efficiency.
We model a nonlinear price curve quoted in a market as the utility indifference curve of a representative liquidity supplier. As the utility function we adopt a g-expectation. In contrast to the standard framework of financial engineering, a trader is no more price taker as any trade has a permanent market impact via a…
The investment economy is a main characteristic of prosperous society. The investment portfolio management is a main financial problem, which has to be solved by the investment, commercial and central banks with the application of modern portfolio theory in the investment economy. We use the learning analytics together…
In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be explicitly and consistently incorporated in the valuation of decisions, using the theory …
We study dynamic allocation problems for discrete time multi-armed bandits under uncertainty, based on the the theory of nonlinear expectations. We show that, under strong independence of the bandits and with some relaxation in the definition of optimality, a Gittins allocation index gives optimal choices. This involve…
New method identifies flawed internal models of the world in animals.
problem How animals make decisions with partial sensory information.
method Generalizes Inverse Rational Control to continuous nonlinear dynamics and noise.
result Identifies the best internal model explaining an agent's actions.
New BED method handles online inference for partially observed dynamical systems.
problem Optimizing data collection for partially observable, partially online dynamical systems.
method Derived estimators of expected information gain and its gradient for SSMs, using nested particle filters.
result Successfully handles both partial observability and online inference in realistic models.
Novel digital twin for complex systems improves performance.
problem Lack of practical implementation details for stochastic nonlinear MDOF systems.
method Decouples time-scales, uses physics-based model, Bayesian filtering, and machine learning.
result Excellent performance of proposed digital twin framework validated by examples.
This work addresses identifiability in sequential data with switching dynamics, introducing a new estimator.
problem Identifiability of sequential data with regime-switching dynamics under flexible assumptions.
method Introduces SDS, a flow-based estimator for exact likelihood optimization.
result Demonstrates improved disentanglement and more accurate forecasting compared to VAE-based estimators.
A new method models financial returns by separating sign and magnitude, improving forecasting accuracy.
problem Capturing nonlinear predictability in financial return dynamics.
method Decomposes returns into sign and magnitude components, using a joint distribution model.
result Significantly outperforms traditional linear models in forecasting U.S. stock market returns.
D2PCCA integrates deep learning and probabilistic modeling for nonlinear dynamical systems.
problem Analyzing nonlinear dynamical systems with probabilistic understanding.
method Combines deep learning and probabilistic modeling, using KL annealing and normalizing flows.
result Captures latent dynamics in sequential datasets with improved convergence and flexibility.