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Portfolio management problems are often divided into two types: active and passive, where the objective is to outperform and track a preselected benchmark, respectively. Here, we formulate and solve a dynamic asset allocation problem that…
Given a universe of N assets, investors often form equally weighted portfolios (EWPs) by selecting subsets of assets. EWPs are simple, robust, and competitive out-of-sample, yet the uncertainty about which subset truly performs best is…
Here and in a follow-on paper, we consider a simple control problem in which the underlying dynamics depend on a parameter $a$ that is unknown and must be learned. In this paper, we assume that $a$ is bounded, i.e., that $|a| \le…
We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local,…
We propose an alternative linearization to the classical Markowitz quadratic portfolio optimization model, based on maximum drawdown. This model, which minimizes maximum portfolio drawdown, is particularly appealing during times of…
Traditional approaches to ensure group fairness in algorithmic decision making aim to equalize ``total'' error rates for different subgroups in the population. In contrast, we argue that the fairness approaches should instead focus only on…
Asset allocation is an investment strategy that aims to balance risk and reward by constantly redistributing the portfolio's assets according to certain goals, risk tolerance, and investment horizon. Unfortunately, there is no simple…
In this paper, both dynamic mean-variance portfolio selection problems and dynamic variance hedging problems are discussed under non-Markovian framework. Explicit closed-loop equilibrium strategies of these problems are respectively…
Investment returns naturally reside on irregular domains, however, standard multivariate portfolio optimization methods are agnostic to data structure. To this end, we investigate ways for domain knowledge to be conveniently incorporated…
We introduce a novel approach to portfolio optimization that leverages hierarchical graph structures and the Schur complement method to systematically reduce computational complexity while preserving full covariance information. Inspired by…
Designing an optimum portfolio for allocating suitable weights to its constituent assets so that the return and risk associated with the portfolio are optimized is a computationally hard problem. The seminal work of Markowitz that attempted…
We consider portfolio selection under nonparametric $\alpha$-maxmin ambiguity in the neighbourhood of a reference distribution. We show strict concavity of the portfolio problem under ambiguity aversion. Implied demand functions are…
The paper predicts an Efficient Market Property for the equity market, where stocks, when denominated in units of the growth optimal portfolio (GP), have zero instantaneous expected returns. Well-diversified equity portfolios are shown to…
We consider a variation on the classical finance problem of optimal portfolio design. In our setting, a large population of consumers is drawn from some distribution over risk tolerances, and each consumer must be assigned to a portfolio of…
Decision making under uncertain environments in the maximization of expected reward while minimizing its risk is one of the ubiquitous problems in many subjects. Here, we introduce a novel problem setting in stochastic bandit optimization…
We consider a simple control problem in which the underlying dynamics depend on a parameter $a$ that is unknown and must be learned. We study three variants of the control problem: Bayesian control, in which we have a prior belief about…
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…
In risk-sharing markets with aggregate uncertainty, characterizing Pareto-optimal allocations when agents might not be risk averse is a challenging task, and the literature has only provided limited explicit results thus far. In particular,…
Given two random realized returns on an investment, which is to be preferred? This is a fundamental problem in finance that has no definitive solution except in the case one investment always returns more than the other. In 1952 Markowitz…
We study entropy-regularized mean-variance portfolio optimization under Bayesian drift uncertainty. Gaussian policies remain optimal under partial information, the value function is quadratic in wealth, and belief-dependent coefficients…