Related papers: Impermanent loss and loss-vs-rebalancing I: some s…
Value-at-Risk (VaR) and Expected Shortfall (ES) are widely used in the financial sector to measure the market risk and manage the extreme market movement. The recent link between the quantile score function and the Asymmetric Laplace…
Model-based reinforcement learning (RL) is more sample efficient than model-free RL by using imaginary trajectories generated by the learned dynamics model. When the model is inaccurate or biased, imaginary trajectories may be deleterious…
The first half of the paper is devoted to description and implementation of statistical tests arguing for the presence of a Brownian component in the inventories and wealth processes of individual traders. We use intra-day data from the…
Balancing weights have been widely applied to single or monotone missingness due to empirical advantages over likelihood-based methods and inverse probability weighting approaches. This paper considers non-monotone missing data under the…
For a random walk defined for a doubly infinite sequence of times, we let the time parameter itself be an integer-valued process, and call the orginal process a random walk at random time. We find the scaling limit which generalizes the…
In this paper, we consider certain $\sigma$-finite measures which can be interpreted as the output of a linear filter. We assume that these measures have regularly varying tails and study whether the input to the linear filter must have…
Fractional Brownian motion (fBm) is a canonical model for long-memory phenomena. In the presence of large amounts of potentially memory-bearing data, the data are often averaged, which can change the structure of the underlying…
Existing regression models tend to fall short in both accuracy and uncertainty estimation when the label distribution is imbalanced. In this paper, we propose a probabilistic deep learning model, dubbed variational imbalanced regression…
This paper continues the examination of inventory control in which the inventory is modelled by a diffusion process and a long-term average cost criterion is used to make decisions. The class of such models under consideration have general…
Algorithms in machine learning and AI do critically depend on at least three key components: (i) the risk function, which is the expectation of the loss function, (ii) the function space, which is often called the hypothesis space, and…
Learning customer preferences from an observed behaviour is an important topic in the marketing literature. Structural models typically model forward-looking customers or firms as utility-maximizing agents whose utility is estimated using…
Since the middle of the 90's, multifractional processes have been introduced for overcoming some limitations of the classical Fractional Brownian Motion model. In their context, the Hurst parameter becomes a Holder continuous function H(?)…
Input-to-state stability (ISS) and $\mathcal{L}_2$-gain are well-known robust stability properties that continue to find wide application in the analysis and control of nonlinear dynamical systems and their interconnections. We investigate…
In order to obviate the requirement of drift dynamics in adaptive dynamic programming (ADP), integral reinforcement learning (IRL) has been proposed as an alternate formulation of Bellman equation.However control coupling dynamics is still…
In this paper we complete and extend our previous work on stochastic control applied to high frequency market-making with inventory constraints and directional bets. Our new model admits several state variables (e.g. market spread,…
We investigate the detailed dynamics of gains and losses made by agents in some kinetic models of wealth exchange. The concept of a walk in an abstract gain-loss space for the agents had been introduced in an earlier work. For models in…
Geometric Mean Market Makers (G3M) such as Uniswap, Sushiswap or Balancer are key building blocks of the nascent Decentralised Finance system. We establish non-arbitrage bounds for the wealth process of such Automated Market Makers in the…
Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…
Long Memory Stochastic volatility (LMSV) models capture two standardized features of financial data: the log-returns are uncorrelated, but their squares, or absolute values are (highly) dependent and they may have heavy tails. EGARCH and…
When outcomes are missing for reasons beyond an investigator's control, there are two different ways to adjust a parameter estimate for covariates that may be related both to the outcome and to missingness. One approach is to model the…