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Motivated by the trade-off between exploitation and exploration in reinforcement learning, we study a continuous-time entropy-regularized mean variance portfolio selection problem in the presence of jumps. We propose an exploratory SDE for…
Portfolio optimization involves determining the optimal allocation of portfolio assets in order to maximize a given investment objective. Traditionally, some form of mean-variance optimization is used with the aim of maximizing returns…
We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…
We study continuous-time portfolio choice with nonlinear payoffs under smooth ambiguity and Bayesian learning. We develop a general framework for dynamic, non-concave asset allocation that accommodates nonlinear payoffs, broad utility…
Different models of capital exchange among economic agents have been proposed recently trying to explain the emergence of Pareto's wealth power law distribution. One important factor to be considered is the existence of risk aversion. In…
We propose and investigate a discrete-time mean field game model involving risk-averse agents. The model under study is a coupled system of dynamic programming equations with a Kolmogorov equation. The agents' risk aversion is modeled by…
Portfolio selection in the periodic investment of securities modeled by a multivariate Merton model with dependent jumps is considered. The optimization framework is designed to maximize expected terminal wealth when portfolio risk is…
Classical mean-variance portfolio theory tells us how to construct a portfolio of assets which has the greatest expected return for a given level of return volatility. Utility theory then allows an investor to choose the point along this…
Merton portfolio management problem is studied in this paper within a stochastic volatility, non constant time discount rate, and power utility framework. This problem is time inconsistent and the way out of this predicament is to consider…
In this paper, we solve the time inconsistent portfolio selection problem by using different utility functions with a moving target as our constraint. We solve this problem by finding an equilibrium control under the given definition as our…
Mean-deviation models, along with the existing theory of coherent risk measures, are well studied in the literature. In this paper, we characterize monotonic mean-deviation (risk) measures from a general mean-deviation model by applying a…
We study a continuous-time Markowitz mean-variance portfolio selection model in which a naive agent, unaware of the underlying time-inconsistency, continuously reoptimizes over time. We define the resulting naive policies through the limit…
Strategies aimed at reducing the negative effects of long-term uncertainty and risk are common in biology, game theory, and finance, even if they entail a cost in terms of mean benefit. Here, we focus on the single mutant's invasion of a…
In this paper we study a time-inconsistent portfolio optimization problem for competitive agents with CARA utilities and non-exponential discounting. The utility of each agent depends on her own wealth and consumption as well as the…
Sequential portfolio selection has attracted increasing interests in the machine learning and quantitative finance communities in recent years. As a mathematical framework for reinforcement learning policies, the stochastic multi-armed…
We propose a general family of piecewise hyperbolic absolute risk aversion (PHARA) utilities, including many classic and non-standard utilities as examples. A typical application is the composition of a HARA preference and a piecewise…
In this study, we address the challenge of portfolio optimization, a critical aspect of managing investment risks and maximizing returns. The mean-CVaR portfolio is considered a promising method due to today's unstable financial market…
This study provides a solution of the equity premium puzzle. Questioning the validity of the Arrow-Pratt measure of relative risk aversion for detecting the risk behavior of investors under all conditions, a new tool, that is, the…
Mean-reverting assets are one of the holy grails of financial markets: if such assets existed, they would provide trivially profitable investment strategies for any investor able to trade them, thanks to the knowledge that such assets…
We propose a novel conditional diffusion model for contextual portfolio optimization that learns the cross-sectional distribution of next-day stock returns conditioned on high-dimensional asset-specific factors. Our model leverages a…