Portfolio Optimization

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 investor. We consider a generalization where the investor tra

The impact of non-deterministic outputs from Large Language Models (LLMs) is not well examined for financial text understanding tasks. Through a compelling case study on investing in the US equity market via news sentiment analysis, we uncover substantial variability in sentence-level sentiment clas

We employ scoring functions, used in statistics for eliciting risk functionals, as cost functions in the Monge-Kantorovich (MK) optimal transport problem. This gives raise to a rich variety of novel asymmetric MK divergences, which subsume the family of Bregman-Wasserstein divergences. We show that

In this paper we model benchmark beating with the increasing convex order (ICX order). The mean constraint in the mean-variance theory of portfolio selection can be regarded as beating a constant. We then investigate the problem of minimizing the variance of a portfolio with ICX order constraints, b

We consider the problem of optimization of contributions of a financial planner such as a working individual towards a financial goal such as retirement. The objective of the planner is to find an optimal and feasible schedule of periodic installments to an investment portfolio set up towards the go

Focusing on gains & losses relative to a risk-free benchmark instead of terminal wealth, we consider an asset allocation problem to maximize time-consistently a mean-risk reward function with a general risk measure which is i) law-invariant, ii) cash- or shift-invariant, and iii) positively homogene

Transaction costs play a critical role in asset allocation and consumption strategies in portfolio management. We apply the methods of dynamic programming and singular perturbation expansion to derive the closed-form leading solutions to this problem for small transaction costs with arbitrary transa

We study the expected utility portfolio optimization problem in an incomplete financial market where the risky asset dynamics depend on stochastic factors and the portfolio allocation is constrained to lie within a given convex set. We employ fundamental duality results from real constrained optimiz

We explore the implications of a preference ordering for an investor-consumer with a strong preference for keeping consumption above an exogenous social norm, but who is willing to tolerate occasional dips below it. We do this by splicing two CRRA preference orderings, one with high curvature below

Turnpike theorems state that if an investor’s utility is asymptotically equivalent to a power utility, then the optimal investment strategy converges to the CRRA strategy as the investment horizon tends to infinity. This paper aims to derive the convergence rates of the turnpike theorem for optimal

In this short note the theory for multivariate asset allocation with elliptically symmetric distributions of returns, as developed in the author’s prior work, is specialized to the case of returns drawn from a multivariate Laplace distribution. This analysis delivers a result closely, but not perfec

In this paper we derive a novel characterization result for time-consistent stochastic control problems with higher-order moments, originally formulated by Wang et al. [SIAM J. Control. Optim., 63 (2025), 1560–1589], and newly explore many solvable instances including a mean-variance-excess kurtosi

We consider a simplified model for optimizing a single-asset portfolio in the presence of transaction costs given a signal with a certain autocorrelation and cross-correlation structure. In our setup, the portfolio manager is given two one-parameter controls to influence the construction of the port

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 relative wealth and consumption to her competitors. Due to the pres

This paper introduces a software component created in Visual Basic for Applications (VBA) that can be applied for creating an optimal portfolio using two different methods. The first method is the seminal approach of Markowitz that is based on finding budget shares via the minimization of the varian

This paper studies the monotone mean-variance (MMV) problem and the classical mean-variance (MV) problem with convex cone trading constraints in a market with random coefficients. We provide semiclosed optimal strategies and optimal values for both problems via certain backward stochastic differenti

An analytical solution to single-horizon asset allocation for an investor with a piecewise-linear utility function, called herein the “budget threshold utility,” and exogenous position limits is presented. The resulting functional form has a surprisingly simple structure and can be readily interpret

We study optimal portfolio choice under Epstein-Zin recursive utility in the presence of general leverage constraints. We first establish that the optimal value function is the unique viscosity solution to the associated Hamilton-Jacobi-Bellman (HJB) equation, by developing a new dynamic programming

This review paper explores the evolution and implementation of target-date funds (TDFs), specifically focusing on their application within the context of Chile’s 2025 pension reform. The introduction of TDFs marks a significant shift in Chile’s pension system, which has traditionally relied on a mul

This paper explores the applications of the 20/60/20 rule-a heuristic method that segments data into top-performing, average-performing, and underperforming groups-in mathematical finance. We review the statistical foundations of this rule and demonstrate its usefulness in risk management and portfo