Related papers: Non-unique time and market incompleteness
We consider a competitive market with risk-averse participants. We assume that agents' risks are measured by coherent risk measures introduced by Artzner et al. (1999). Fundamental theorems of welfare economics have long established the…
The efficiency of a modern economy depends on what we call the Value-Tracking Hypothesis: that market prices of key assets broadly track some underlying value. This can be expected if a sufficient weight of market participants are…
The objective is to develop a general stochastic approach to delays on financial markets. We suggest such a concept in the context of large platonic markets, which allow infinitely many assets and incorporate a restricted information…
The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be…
The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation)…
This paper studies optimal market making for large-tick assets in the presence of latency. We consider a random walk model for the asset price, and formulate the market maker's optimization problem using Markov Decision Processes (MDP). We…
A market model in Stochastic Portfolio Theory is a finite system of strictly positive stochastic processes. Each process represents the capitalization of a certain stock. If at any time no stock dominates almost the entire market, which…
It has been understood that the "local" existence of the Markowitz' optimal portfolio or the solution to the local-risk minimization problem is guaranteed by some specific mathematical structures on the underlying assets price processes…
We develop a new market-making model, from the ground up, which is tailored towards high-frequency trading under a limit order book (LOB), based on the well-known classification of order types in market microstructure. Our flexible…
Markets have internal dynamics leading to excess volatility and other phenomena that are difficult to explain using rational expectations models. This paper studies these using a nonequilibrium price formation rule, developed in the context…
Norms of Persistent Homology introduced in topological data analysis are seen as indicators of system instability, analogous to the changing predictability that is captured in financial market uncertainty indexes. This paper demonstrates…
In the paper, the martingales and super-martingales relative to a regular set of measures are systematically studied. The notion of local regular super-martingale relative to a set of equivalent measures is introduced and the necessary and…
With increasing competition and pace in the financial markets, robust forecasting methods are becoming more and more valuable to investors. While machine learning algorithms offer a proven way of modeling non-linearities in time series,…
An explicit formula is derived for the value of weak information in a discrete time model that works for a wide range of utility functions including the logarithmic and power utility. We assume a complete market with a finite number of…
We introduce a discrete binary tree for pricing contingent claims with the underlying security prices exhibiting history dependence characteristic of that induced by market microstructure phenomena. Example dependencies considered include…
It has been suggested that marked point processes might be good candidates for the modelling of financial high-frequency data. A special class of point processes, Hawkes processes, has been the subject of various investigations in the…
In practice there are temporary arbitrage opportunities arising from the fact that prices for a given asset at different stock exchanges are not instantaneously the same. We will show that even in such an environment there exists a…
Through the analysis of a dataset of ultra high frequency order book updates, we introduce a model which accommodates the empirical properties of the full order book together with the stylized facts of lower frequency financial data. To do…
We measure the influence of different time-scales on the dynamics of financial market data. This is obtained by decomposing financial time series into simple oscillations associated with distinct time-scales. We propose two new time-varying…
We study an optimal execution problem with uncertain market impact to derive a more realistic market model. We construct a discrete-time model as a value function for optimal execution. Market impact is formulated as the product of a…