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We study a problem of finding an optimal stopping strategy to liquidate an asset with unknown drift. Taking a Bayesian approach, we model the initial beliefs of an individual about the drift parameter by allowing an arbitrary probability…

Mathematical Finance · Quantitative Finance 2015-09-03 Erik Ekström , Juozas Vaicenavicius

We consider a stochastic control model driven by a fractional Brownian motion. This model is a formal approximation to a queueing network with an on-off input process. We study stochastic control problems associated with the long-run…

Probability · Mathematics 2008-08-12 Arka P. Ghosh , Alexander Roitershtein , Ananda Weerasinghe

We study the problem of dynamically trading a futures contract and its underlying asset under a stochastic basis model. The basis evolution is modeled by a stopped scaled Brownian bridge to account for non-convergence of the basis at…

Portfolio Management · Quantitative Finance 2019-05-28 Bahman Angoshtari , Tim Leung

In this paper we solve the hedge fund manager's optimization problem in a model that allows for investors to enter and leave the fund over time depending on its performance. The manager's payoff at the end of the year will then depend not…

Portfolio Management · Quantitative Finance 2014-03-04 Moritz Duembgen , L. C. G. Rogers

We study a stochastic recursive optimal control problem in which the cost functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Some of the economic and financial optimization…

Optimization and Control · Mathematics 2015-09-01 Mingshang Hu , Shaolin Ji

Liquidation is the process of selling a large number of shares of one stock sequentially within a given time frame, taking into consideration the costs arising from market impact and a trader's risk aversion. The main challenge in…

Trading and Market Microstructure · Quantitative Finance 2019-06-27 Wenhang Bao , Xiao-yang Liu

The Black-Litterman model is a framework for incorporating forward-looking expert views in a portfolio optimization problem. Existing work focuses almost exclusively on single-period problems with the forecast horizon matching that of the…

Portfolio Management · Quantitative Finance 2025-04-17 Anas Abdelhakmi , Andrew Lim

We study an optimal execution strategy for purchasing a large block of shares over a fixed time horizon. The execution problem is subject to a general price impact that gradually dissipates due to market resilience. We allow for general…

Mathematical Finance · Quantitative Finance 2026-04-14 Etienne Chevalier , Yadh Hafsi , Vathana Ly Vath , Sergio Pulido

We find the variance-optimal equivalent martingale measure when multivariate assets are modeled by a regime-switching geometric Brownian motion, and the regimes are represented by a homogeneous continuous time Markov chain. Under this new…

Probability · Mathematics 2023-09-14 Bruno Remillard , Sylvain Rubenthaler

This paper studies an optimal trading problem that incorporates the trader's market view on the terminal asset price distribution and uninformative noise embedded in the asset price dynamics. We model the underlying asset price evolution by…

Mathematical Finance · Quantitative Finance 2018-08-07 Tim Leung , Jiao Li , Xin Li

We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that…

Trading and Market Microstructure · Quantitative Finance 2014-12-16 Takashi Kato

We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…

Probability · Mathematics 2016-07-26 Viktor Bezborodov , Luca Di Persio , Yuliya Mishura

The aim of this paper is to present the new results concerning some functionals of Brownian motion with drift and present their applications in financial mathematics. We find a probabilistic representation of the Laplace transform of…

Probability · Mathematics 2011-02-02 Jacek Jakubowski , Maciej Wisniewolski

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…

Physics and Society · Physics 2009-11-13 Javier Villarroel

This paper studies the finite horizon portfolio management by optimally tracking a ratcheting capital benchmark process. It is assumed that the fund manager can dynamically inject capital into the portfolio account such that the total…

Portfolio Management · Quantitative Finance 2021-05-03 Lijun Bo , Huafu Liao , Xiang Yu

We study a finite-horizon stochastic control criterion for non-convex optimization in which Brownian exploration is balanced against a quadratic control cost. Rather than emphasizing the classical Hopf--Cole representation, we isolate the…

Optimization and Control · Mathematics 2026-05-26 Qin Li , Sixu Li , Eitan Tadmor , Emmanuel Trélat

The first half of the paper is devoted to description and implementation of statistical tests arguing for the presence of a Brownian component in the inventories and wealth processes of individual traders. We use intra-day data from the…

Trading and Market Microstructure · Quantitative Finance 2021-05-03 Rene Carmona , Laura Leal

We consider the problem of utility maximization for investors with power utility functions. Building on the earlier work Larsen et al. (2016), we prove that the value of the problem is a Frechet-differentiable function of the drift of the…

Mathematical Finance · Quantitative Finance 2017-03-28 Huy N. Chau , Miklos Rasonyi

We continue the analysis of our previous paper (Czichowsky/Schachermayer/Yang 2014) pertaining to the existence of a shadow price process for portfolio optimisation under proportional transaction costs. There, we established a positive…

Mathematical Finance · Quantitative Finance 2016-08-05 Christoph Czichowsky , Rémi Peyre , Walter Schachermayer , Junjian Yang

We investigate the general problem of how to model the kinematics of stock prices without considering the dynamical causes of motion. We propose a stochastic process with long-range correlated absolute returns. We find that the model is…

Disordered Systems and Neural Networks · Physics 2008-12-02 M. Serva , U. L. Fulco , M. L. Lyra , G. M. Viswanathan