Related papers: A note on Almgren-Chriss optimal execution problem…
We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that…
We develop a systematic framework for the model reduction of multivariate geometric Brownian motions (GBMs), a fundamental class of stochastic processes with broad applications in mathematical finance, population biology, and statistical…
In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift…
In the previous paper (Inverse Problems, 32, 015010, 2016), a new heuristic mathematical model was proposed for accurate forecasting of prices of stock options for 1-2 trading days ahead of the present one. This new technique uses the…
In the present paper, we study the optimal execution problem under stochastic price recovery based on limit order book dynamics. We model price recovery after execution of a large order by accelerating the arrival of the refilling order,…
We extend the theory of asymmetric information in mispricing models for stocks following geometric Brownian motion to constant relative risk averse investors. Mispricing follows a continuous mean--reverting Ornstein--Uhlenbeck process.…
In the seminal paper on optimal execution of portfolio transactions, Almgren and Chriss (2001) define the optimal trading strategy to liquidate a fixed volume of a single security under price uncertainty. Yet there exist situations, such as…
We study the problem of dynamically trading futures in a regime-switching market. Modeling the underlying asset price as a Markov-modulated diffusion process, we present a utility maximization approach to determine the optimal futures…
We consider the problem of tracking a target whose dynamics is modeled by a continuous It\=o semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds…
In this article we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market…
We show that the unique solution to a semilinear stochastic differential equation with almost periodic coefficients driven by a fractional Brownian motion is almost periodic in a sense related to random dynamical systems. This type of…
It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysics framework for…
We derive closed-form solutions to the optimal stopping problems related to the pricing of perpetual American standard and lookback put and call options in the extensions of the Black-Merton-Scholes model with progressively enlarged…
This article analyzes the behavior of a Brownian fluctuation process under a mixed strategic game setup. A variant of a compound Brownian motion has been newly proposed, which is called the Shifted Brownian Fluctuation Process to predict…
We propose a framework to study the optimal liquidation strategy in a limit order book for large-tick stocks, with spread equal to one tick. All order book events (market orders, limit orders and cancellations) occur according to…
We study optimal investment problem for a diffusion market consisting of a finite number of risky assets (for example, bonds, stocks and options). Risky assets evolution is described by Ito's equation, and the number of risky assets can be…
Modeling financial data often relies on assumptions that may prove insufficient or unrealistic in practice. The Geometric Brownian Motion (GBM) model is frequently employed to represent stock price processes. This study investigates whether…
We study an optimal extraction problem where the agent's actions in the spot market exert an additive proportional negative impact on the commodity price. The commodity price dynamics, prior to any activity by the agent, are evolved by a…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
The paper studies intraday price movement of stocks that is considered as an image classification problem. Using a CNN-based model we make a compelling case for the high-level relationship between the first hour of trading and the close.…