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We analyze the martingale selection problem of Rokhlin (2006) in a pointwise (robust) setting. We derive conditions for solvability of this problem and show how it is related to the classical no-arbitrage deliberations. We obtain versions…
Consider an agent who enters a financial market on day t = 0 with an initial capital amount x. He invests this amount on stocks and the money market, and by day t = T, has generated a wealth W . He is given a convex class of probability…
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Mean-reverting portfolios with volatility and sparsity constraints are of prime interest to practitioners in finance since they are both profitable and well-diversified, while also managing risk and minimizing transaction costs. Three main…
The general method is proposed for constructing a family of martingale measures for a wide class of evolution of risky assets. The sufficient conditions are formulated for the evolution of risky assets under which the family of equivalent…
We extend the classical mean-variance (MV) framework and propose a robust and sparse portfolio selection model incorporating an ellipsoidal uncertainty set to reduce the impact of estimation errors and fixed transaction costs to penalize…
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In this paper, we consider $n$ agents who invest in a general financial market that is free of arbitrage and complete. The aim of each investor is to maximize her expected utility while ensuring, with a specified probability, that her…
The model of this paper gives a convenient strategy that a bank in the federal funds market can use in order to maximize its profit in a contemporaneous reserve requirement (CRR) regime. The reserve requirements are determined by the demand…
We consider a problem of optimal investment with intermediate consumption in the framework of an incomplete semimartingale model of a financial market. We show that a necessary and sufficient condition for the validity of key assertions of…
This paper studies a type of periodic utility maximization for portfolio management in an incomplete market model, where the underlying price diffusion process depends on some external stochastic factors. The portfolio performance is…
In this paper we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following…
We characterize absence of arbitrage with simple trading strategies in a discounted market with a constant bond and several risky assets. We show that if there is a simple arbitrage, then there is a 0-admissible one or an obvious one, that…
We estimate the global minimum variance (GMV) portfolio in the high-dimensional case using results from random matrix theory. This approach leads to a shrinkage-type estimator which is distribution-free and it is optimal in the sense of…
We consider the Brownian market model and the problem of expected utility maximization of terminal wealth. We, specifically, examine the problem of maximizing the utility of terminal wealth under the presence of transaction costs of a…
The presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the…
In this article, we show necessary and sufficient conditions for a function to transform a continuous Markov semimartingale to a semimartingale. As a result, the no-arbitrage principle guarantees the differentiability of asset prices with…
This paper concerns the numerical solution of a fully nonlinear parabolic double obstacle problem arising from a finite portfolio selection with proportional transaction costs. We consider the optimal allocation of wealth among multiple…
We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it…
We address a portfolio selection problem that combines active (outperformance) and passive (tracking) objectives using techniques from convex analysis. We assume a general semimartingale market model where the assets' growth rate processes…