Related papers: Time Consistent Dynamic Limit Order Books Calibrat…
We study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of…
Safe navigation in dynamic environments remains challenging due to uncertain obstacle behaviors and the lack of formal prediction guarantees. We propose two motion planning frameworks that leverage conformal prediction (CP): a global…
In this paper we present a theoretical framework for determining dynamic ask and bid prices of derivatives using the theory of dynamic coherent acceptability indices in discrete time. We prove a version of the First Fundamental Theorem of…
This paper proposes an alternative to the classical price-adjustment mechanism (called "t\^{a}tonnement" after Walras) that is second-order in time. The proposed mechanism, an analogue to the damped harmonic oscillator, provides a dynamic…
This paper studies the fill probabilities of limit orders placed at different price levels in a limit order book. These probabilities play a central role in execution optimization, as limit orders are not guaranteed to be executed and…
In this paper, we develop a method to automatically generate a control policy for a dynamical system modeled as a Markov Decision Process (MDP). The control specification is given as a Linear Temporal Logic (LTL) formula over a set of…
This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modelled by a (possibly uncountable) family of price processes on the same probability space. Our…
We propose \textbf{Temporal Conformal Prediction (TCP)}, a distribution-free framework for constructing well-calibrated prediction intervals in nonstationary time series. TCP couples a modern quantile forecaster with a rolling…
Before delegating a task to an autonomous system, a human operator may want a guarantee about the behavior of the system. This paper extends previous work on conformal prediction for functional data and conformalized quantile regression to…
This paper shows that temporal CNNs accurately predict bitcoin spot price movements from limit order book data. On a 2 second prediction time horizon we achieve 71\% walk-forward accuracy on the popular cryptocurrency exchange coinbase. Our…
We develop a timeout based extension of propositional linear temporal logic (which we call TLTL) to specify timing properties of timeout based models of real time systems. TLTL formulas explicitly refer to a running global clock together…
We investigate a model for planning under uncertainty with temporallyextended actions, where multiple actions can be taken concurrently at each decision epoch. Our model is based on the options framework, and combines it with factored state…
This paper considers a Markovian model of a limit order book where time-dependent rates are allowed. With the objective of understanding the mechanisms through which a microscopic model of an orderbook can converge to more general diffusion…
In this paper, we consider a continuous-time Markov decision process (CTMDP) in Borel spaces, where the certainty equivalent with respect to the exponential utility of the total undiscounted cost is to be minimized. The cost rate is…
In this paper we consider classes of models that have been recently developed for quantitative finance that involve modelling a highly complex multivariate, multi-attribute stochastic process known as the Limit Order Book (LOB). The LOB is…
We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional…
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options…
The paper studies sub and super-replication price bounds for contingent claims defined on general trajectory based market models. No prior probabilistic or topological assumptions are placed on the trajectory space, trading is assumed to…
This paper shows that in suitable markets, even with out-of-equilibrium trade allowed, a simple price update rule leads to rapid convergence toward the equilibrium. In particular, this paper considers a Fisher market repeated over an…
We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson…