Related papers: Time consistency of the mean-risk problem
Portfolio optimization is an important process in finance that consists in finding the optimal asset allocation that maximizes expected returns while minimizing risk. When assets are allocated in discrete units, this is a combinatorial…
This paper explores the practical approach to portfolio selection methods for investments. The study delves into portfolio theory, discussing concepts such as expected return, variance, asset correlation, and opportunity sets. It also…
A highly relevant problem of modern finance is the design of Value-at-Risk (VaR) optimal portfolios. Due to contemporary financial regulations, banks and other financial institutions are tied to use the risk measure to control their credit,…
Portfolio optimization emerged with the seminal paper of Markowitz (1952). The original mean-variance framework is appealing because it is very efficient from a computational point of view. However, it also has one well-established failing…
In matter of Portfolio selection, we consider a generalization of the Markowitz Mean-Variance model which includes buy-in threshold constraints. These constraints limit the amount of capital to be invested in each asset and prevent very…
In this paper we propose a new methodology for solving an uncertain stochastic Markovian control problem in discrete time. We call the proposed methodology the adaptive robust control. We demonstrate that the uncertain control problem under…
We show that the Markowitz portfolio is a scalar multiple of another portfolio which replaces the covariance with the second moment matrix, via simple application of the Sherman-Morrison identity. Moreover it is shown that when using…
This paper studies the mean-variance optimal portfolio choice of an investor pre-committed to a deterministic investment policy in continuous time in a market with mean-reversion in the risk-free rate and the equity risk-premium. In the…
In this paper, we present a discretization algorithm for finite horizon risk constrained dynamic programming algorithm in [Chow_Pavone_13]. Although in a theoretical standpoint, Bellman's recursion provides a systematic way to find optimal…
We consider the problem of portfolio selection within the classical Markowitz mean-variance framework, reformulated as a constrained least-squares regression problem. We propose to add to the objective function a penalty proportional to the…
Modeling and managing portfolio risk is perhaps the most important step to achieve growing and preserving investment performance. Within the modern portfolio construction framework that built on Markowitz's theory, the covariance matrix of…
In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider…
A continuous-time Markowitz's mean-variance portfolio selection problem is studied in a market with one stock, one bond, and proportional transaction costs. This is a singular stochastic control problem,inherently in a finite time horizon.…
We present the unified market-based description of returns and variances of the trades with shares of a particular security, of the trades with shares of all securities in the market, and of the trades with the market portfolio. We consider…
This paper studies a mean-risk portfolio choice problem for log-returns in a continuous-time, complete market. This is a growth-optimal problem with risk control. The risk of log-returns is measured by weighted Value-at-Risk (WVaR), which…
We develop an approach for solving time-consistent risk-sensitive stochastic optimization problems using model-free reinforcement learning (RL). Specifically, we assume agents assess the risk of a sequence of random variables using dynamic…
Instead of controlling "symmetric" risks measured by central moments of investment return or terminal wealth, more and more portfolio models have shifted their focus to manage "asymmetric" downside risks that the investment return is below…
Portfolio diversification is one of the most effective ways to minimize investment risk. Individuals and fund managers aim to create a portfolio of assets that not only have high returns but are also uncorrelated. This goal can be achieved…
This paper focuses on a dynamic multi-asset mean-variance portfolio selection problem under model uncertainty. We develop a continuous time framework for taking into account ambiguity aversion about both expected return rates and…
We consider a multi-objective risk-averse two-stage stochastic programming problem with a multivariate convex risk measure. We suggest a convex vector optimization formulation with set-valued constraints and propose an extended version of…