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Performing signal processing over graphs requires knowledge of the underlying fixed topology. However, graphs often grow in size with new nodes appearing over time, whose connectivity is typically unknown; hence, making more challenging the…
This short note provides a systematic construction of market models without unbounded profits but with arbitrage opportunities.
In this paper, we consider an anticipative nonlinear filtering problem, in which the observation noise is correlated with the past of the signal. This new signal-observation model has its applications in both finance models with insider…
In this paper, we present a method of estimating the volatility of a signal that displays stochastic noise (such as a risky asset traded on an open market) utilizing Linear Predictive Coding. The main purpose is to associate volatility with…
We describe an end-to-end real-time S&P futures trading system. Inner-shell stochastic nonlinear dynamic models are developed, and Canonical Momenta Indicators (CMI) are derived from a fitted Lagrangian used by outer-shell trading models…
The behaviour of a space-modulated, so-called "argumental" oscillator is studied, which is represented by a model having an even-parity space-modulating function. Analytic expressions of a stability criterion and of discrete energy levels…
The potential of machine learning to automate and control nonlinear, complex systems is well established. These same techniques have always presented potential for use in the investment arena, specifically for the managing of equity…
These are course notes on the application of SDEs to options pricing. The author was partially supported by NSF grant DMS-0739195.
The study efforts to explore and extend the crisis predictability by synthetically reviewing and comparing a full mixture of early warning models into two constitutions: crisis identifications and predictive models. Given empirical results…
Changes in market conditions present challenges for investors as they cause performance to deviate from the ranges predicted by long-term averages of means and covariances. The aim of conditional asset allocation strategies is to overcome…
We use a path integral approach for solving the stochastic equations underlying the financial markets, and we show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the…
Data analytics software applications have become an integral part of the decision-making process of analysts. Users of such a software face challenges due to insufficient product and domain knowledge, and find themselves in need of help. To…
We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the…
Algorithm of multicurrency trading at the market of Forex is realized on the basis of nonlinear stochastic wavelets. The distinctive feature of the algorithm is the possibility of weakly- and strongly connected horizontal self-assemblies,…
This paper addresses sensitivity analysis for dynamic models, linking dependent inputs to observed outputs. The usual method to estimate Sobol indices are based on the independence of input variables. We present a method to overpass this…
Trading frictions are stochastic. They are, moreover, in many instances fast-mean reverting. Here, we study how to optimally trade in a market with stochastic price impact and study approximations to the resulting optimal control problem…
This paper introduces an approach to gas-like models, from the concept of entropy, using the money stock data of two economic agents, in this case of two countries, which carry out market actions (trading) in two theoretical scenarios: in…
In this paper, we present a method for constructing a (static) portfolio of co-maturing European options whose price sign is determined by the skewness level of the associated implied volatility. This property holds regardless of the…
We discuss a method for predicting financial movements and finding pockets of predictability in the price-series, which is built around inferring the heterogeneity of trading strategies in a multi-agent trader population. This work explores…
We propose a general non-linear order book model that is built from the individual behaviours of the agents. Our framework encompasses Markovian and Hawkes based models. Under mild assumptions, we prove original results on the ergodicity…