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An agnostic PAC learning algorithm finds a predictor that is competitive with the best predictor in a benchmark hypothesis class, where competitiveness is measured with respect to a given loss function. However, its predictions might be…
Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean…
This paper studies a continuous-time portfolio selection problem under a general distribution of random risk aversion (RRA). We provide a complete characterization of all deterministic equilibrium strategies in closed form. Our results show…
Motivated by recent advances in the spectral theory of auto-covariance matrices, we are led to revisit a reformulation of Markowitz' mean-variance portfolio optimization approach in the time domain. In its simplest incarnation it applies to…
Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two dimensional space…
We consider the issue of solution uniqueness for portfolio optimization problem and its inverse for asset returns with a finite number of possible scenarios. The risk is assessed by deviation measures introduced by [Rockafellar et al.,…
In portfolio risk minimization, the inverse covariance matrix of returns is often unknown and has to be estimated in practice. This inverse covariance matrix also prescribes the hedge trades in which a stock is hedged by all the other…
Using daily returns of the S&P 500 stocks from 2001 to 2011, we perform a backtesting study of the portfolio optimization strategy based on the extreme risk index (ERI). This method uses multivariate extreme value theory to minimize the…
In this article we consider a special case of an optimal consumption/optimal portfolio problem first studied by Constantinides and Magill and by Davis and Norman, in which an agent with constant relative risk aversion seeks to maximise…
In this paper, we derive the feasibility conditions for the robust counterparts of the uncertain Markowitz model. Our study is based on ellipsoidal, box, polyhedral uncertainty sets and also the uncertainty sets obtained from their…
In this paper we present an evolutionary optimization approach to solve the risk parity portfolio selection problem. While there exist convex optimization approaches to solve this problem when long-only portfolios are considered, the…
This study develops an inverse portfolio optimization framework for recovering latent investor preferences including risk aversion, transaction cost sensitivity, and ESG orientation from observed portfolio allocations. Using controlled…
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…
This paper is concerned with the uniqueness issue of open-loop equilibrium investment strategies of dynamic mean-variance portfolio selection problems with random coefficients. A unified method is developed to treat both the problems with…
We study an optimal liquidation problem under the ambiguity with respect to price impact parameters. Our main results show that the value function and the optimal trading strategy can be characterized by the solution to a semi-linear PDE…
We give an algebraic definition of a Markowitz market and classify markets up to isomorphism. Given this classification, the theory of portfolio optimization in Markowitz markets without short selling constraints becomes trivial.…
Statistical learning theory and the Probably Approximately Correct (PAC) criterion are the common approach to mathematical learning theory. PAC is widely used to analyze learning problems and algorithms, and have been studied thoroughly.…
Auctions in which agents' payoffs are random variables have received increased attention in recent years. In particular, recent work in algorithmic mechanism design has produced mechanisms employing internal randomization, partly in…
As the cornerstone of modern portfolio theory, Markowitz's mean-variance optimization is considered a major model adopted in portfolio management. However, due to the difficulty of estimating its parameters, it cannot be applied to all…
The conventional wisdom of mean-variance (MV) portfolio theory asserts that the nature of the relationship between risk and diversification is a decreasing asymptotic function, with the asymptote approximating the level of portfolio…