arXiv research

New bounds for adaptive control in high dimensions without fixed state space.

We study the performance of the certainty equivalent controller on Linear Quadratic (LQ) control problems with unknown transition dynamics. We show that for both the fully and partially observed settings, the sub-optimality gap between the cost incurred by playing the certainty equivalent controller on the true system …

New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first "regulator" version is independent from any market model whereas the second version, called the market extension, takes trading …

Study on implied certainty equivalent rates in financial markets and electric vehicles.

New algorithm minimizes regret in unknown LQ control systems.

Study shows certainty equivalent policy minimizes regret in continuous-time systems.

The effectiveness of model-based versus model-free methods is a long-standing question in reinforcement learning (RL). Motivated by recent empirical success of RL on continuous control tasks, we study the sample complexity of popular model-based and model-free algorithms on the Linear Quadratic Regulator (LQR). We show…

We consider the problem of online adaptive control of the linear quadratic regulator, where the true system parameters are unknown. We prove new upper and lower bounds demonstrating that the optimal regret scales as $\widetildeΘ({\sqrt{d_{\mathbf{u}}^2 d_{\mathbf{x}} T}})$, where $T$ is the number of time steps, $d_{\m…

The paper develops a new approach to conditional risk measures using modular convex analysis.

Solves Merton's investment-consumption problem with certainty equivalent approach.

Overview of risk-sensitive Markov decision processes with Optimized Certainty Equivalent.

We study a security threat to batch reinforcement learning and control where the attacker aims to poison the learned policy. The victim is a reinforcement learner / controller which first estimates the dynamics and the rewards from a batch data set, and then solves for the optimal policy with respect to the estimates. …

Study risk-sensitive market making with entropy regularization for better quote control.

For incomplete preference relations that are represented by multiple priors and/or multiple -- possibly multivariate -- utility functions, we define a certainty equivalent as well as the utility buy and sell prices and indifference price bounds as set-valued functions of the claim. Furthermore, we motivate and introduc…

Study task-guided exploration in linear dynamical systems, improving sample complexity.

Deep learning solves dynamic programming with recursive utility.

The paper analyzes risk estimation methods and derives bounds for OCE risk.

Introduces new performance measures using scaled utility functions.

Model shows incentives in shared order book can lead to free-rider problem.

Study scaling limits for option pricing in trinomial models.

CEFOL uses deep learning for dynamic programming with recursive utility.

Proposes a new method to rank risky investments based on Omega measure.

We consider the class of risk measures associated with optimized certainty equivalents. This class includes several popular examples, such as CV@R and monotone mean-variance. Numerical schemes are developed for the computation of these risk measures using Fourier transform methods. This leads, in particular, to a very …

New multivariate risk measures improve on univariate OCE methods.

Study risk-sensitive reinforcement learning with optimized certainty equivalents.

New robust control method for uncertain systems using bootstrapped noise.

This work uses a scalable approach to identify partially observed nonlinear systems.

Study optimal investment decisions for diverse risk-tolerant agents.

We consider the problem of optimal risk sharing in a pool of cooperative agents. We analyze the asymptotic behavior of the certainty equivalents and risk premia associated with the Pareto optimal risk sharing contract as the pool expands. We first study this problem under expected utility preferences with an objectivel…

This paper introduces new risk measures for evaluating losses with varying time horizons.

The paper develops robust risk measures for uncertain loss positions.

This paper studies the optimal risk-averse timing to sell a risky asset. The investor's risk preference is described by the exponential, power, or log utility. Two stochastic models are considered for the asset price -- the geometric Brownian motion and exponential Ornstein-Uhlenbeck models -- to account for, respectiv…

Submodularity is studied for convex risk measures, including Expected Shortfall.

We consider a model in which a trader aims to maximize expected risk-adjusted profit while trading a single security. In our model, each price change is a linear combination of observed factors, impact resulting from the trader's current and prior activity, and unpredictable random effects. The trader must learn coeffi…

Optimized certainty equivalents (OCEs) is a family of risk measures widely used by both practitioners and academics. This is mostly due to its tractability and the fact that it encompasses important examples, including entropic risk measures and average value at risk. In this work we consider stochastic optimal control…

This paper tackles adaptive control of unknown Markov jump systems with sample complexity and regret bounds.

Model proposes how regulators should oversee complex algorithms in high-stakes applications.

Regulated curves on Banach manifolds with continuous projections and regulated derivatives are studied.

Accounting for model uncertainty in risk management and option pricing leads to infinite dimensional optimization problems which are both analytically and numerically intractable. In this article we study when this hurdle can be overcome for the so-called optimized certainty equivalent risk measure (OCE) -- including t…

Appropriate traffic regulations, e.g. planned road closure, are important in congested events. Crowd simulators have been used to find appropriate regulations by simulating multiple scenarios with different regulations. However, this approach requires multiple simulation runs, which are time-consuming. In this paper, w…

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 show that any objective risk measurement algorithm mandated by central banks for regulated financial entities will result in more risk being taken on by those financial entities than would otherwise be the case. Furthermore, the risks taken on by the regulated financial entities are far more systemically concentrate…

New mechanism designs regulate herding in financial markets.

This paper shows CEM is a special case of TTM, leading to new proofs and improved sample complexity bounds.

We present a simulation-and-regression method for solving dynamic portfolio allocation problems in the presence of general transaction costs, liquidity costs and market impacts. This method extends the classical least squares Monte Carlo algorithm to incorporate switching costs, corresponding to transaction costs and t…

In a market system, regulations are designed to prevent or rectify market failures that inhibit fair exchange, such as monopoly or transactions with hidden costs. Because regulations reduce profits to those possessing unfair advantage, these advantaged corporations (whether individuals, companies, or other collective o…

The paper studies risk-sensitive learning schemes and provides learning bounds for empirical OCE minimizers.

MiCA regulation led to a shift in stablecoin dominance.