相关论文: Binary market models with memory

We consider a general class of continuous asset price models where the drift and the volatility functions, as well as the driving Brownian motions, change at a random time $\tau$. Under minimal assumptions on the random time and on the…

We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in discrete time. In particular, we prove a Fundamental Theorem of Asset Pricing and a Superhedging Theorem,…

We consider a financial market where the asset price follows a fractional Brownian motion. We introduce a family of investment strategies, and quantify profit possibilities for both persistent and antipersistant markets.

Markets composed of stocks with capitalization processes represented by positive continuous semimartingales are studied under the condition that the market excess growth rate is bounded away from zero. The following examples of these…

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 infinite dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide a dual characterization of the super-replication cost.…

We study a robust stochastic optimization problem in the quasi-sure setting in discrete-time. We show that under a lineality-type condition the problem admits a maximizer. This condition is implied by the no-arbitrage condition in models of…

We construct a binomial tree model fitting all moments to the approximated geometric Brownian motion. Our construction generalizes the classical Cox-Ross-Rubinstein, the Jarrow-Rudd, and the Tian binomial tree models. The new binomial model…

Motivated by the Corns-Satchell, continuous time, option pricing model, we develop a binary tree pricing model with underlying asset price dynamics following It\^o-Mckean skew Brownian motion. While the Corns-Satchell market model is…

This paper builds a model of interactive belief hierarchies to derive the conditions under which judging an arbitrage opportunity requires Bayesian market participants to exercise their higher-order beliefs. As a Bayesian, an agent must…

In this paper, we derive and analyze a continuous of a binary option market with exogenous information. The resulting non-linear system has a discontinuous right hand side, which can be analyzed using zero-dimensional Filippov surfaces.…

We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…

In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker…

Recent studies have identified long-range dependence as a key feature in the dynamics of both mortality and interest rates. Building on this insight, we develop a novel bi-variate stochastic framework based on mixed fractional Brownian…

We propose to study market efficiency from a computational viewpoint. Borrowing from theoretical computer science, we define a market to be \emph{efficient with respect to resources $S$} (e.g., time, memory) if no strategy using resources…

We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise…

In this paper we provide a quantitative analysis to the concept of arbitrage, that allows to deal with model uncertainty without imposing the no-arbitrage condition. In markets that admit ``small arbitrage", we can still make sense of the…

We consider a simple binary market model containing $N$ competitive agents. The novel feature of our model is that it incorporates the tendency shown by traders to look for patterns in past price movements over multiple time scales, i.e.…

In this work, we aim to design a data marketplace; a robust real-time matching mechanism to efficiently buy and sell training data for Machine Learning tasks. While the monetization of data and pre-trained models is an essential focus of…

We discuss how minimal financial market models can be constructed by bridging the gap between two existing, but incomplete, market models: a model in which a population of virtual traders make decisions based on common global information…