Related papers: The geometry of relative arbitrage
Portfolio selection problems that optimize expected utility are usually difficult to solve. If the number of assets in the portfolio is large, such expected utility maximization problems become even harder to solve numerically. Therefore,…
We characterize the minimal time horizon over which any equity market with $d \geq 2$ stocks and sufficient intrinsic volatility admits relative arbitrage with respect to the market portfolio. If $d \in \{2,3\}$, the minimal time horizon…
We study Atlas-type models of equity markets with local characteristics that depend on both name and rank, and in ways that induce a stable capital distribution. Ergodic properties and rankings of processes are examined with reference to…
The optimization of large portfolios displays an inherent instability to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in…
We show that in an equity market model with Knightian uncertainty regarding the relative risk and covariance structure of its assets, the arbitrage function -- defined as the reciprocal of the highest return on investment that can be…
Portfolio sorting is ubiquitous in the empirical finance literature, where it has been widely used to identify pricing anomalies. Despite its popularity, little attention has been paid to the statistical properties of the procedure. We…
This paper considers the constrained portfolio optimization in a generalized life-cycle model. The individual with a stochastic income manages a portfolio consisting of stocks, a bond, and life insurance to maximize his or her consumption…
In the standard equilibrium and/or arbitrage pricing framework, the value of any asset is uniquely specified from the belief that only the systematic risks need to be remunerated by the market. Here, we show that, even for arbitrary large…
I find a topological arrangement of stocks traded in a financial market which has associated a meaningful economic taxonomy. The topological space is a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting…
This paper studies the problem of maximizing expected utility from terminal wealth in a semi-static market composed of derivative securities, which we assume can be traded only at time zero, and of stocks, which can be traded continuously…
This paper presents a synthesis of the theories of portfolio generating functions and option pricing. The theory of portfolio generation is extended to measure the value of portfolios generated by positive C^{2,1} functions of asset prices…
We derive valuations of a portfolio of financial instruments from a securities lending perspective, under different assumptions, and show a weighting scheme that converges to the true valuation. We illustrate conditions under which our…
In order to find a way of measuring the degree of incompleteness of an incomplete financial market, the rank of the vector price process of the traded assets and the dimension of the associated acceptance set are introduced. We show that…
We consider a continuous-time market with proportional transaction costs. Under appropriate assumptions we prove the existence of optimal strategies for investors who maximize their worst-case utility over a class of possible models. We…
This paper introduces a new functional optimization approach to portfolio optimization problems by treating the unknown weight vector as a function of past values instead of treating them as fixed unknown coefficients in the majority of…
We study the range of prices at which a rational agent should contemplate transacting a financial contract outside a given securities market. Trading is subject to nonproportional transaction costs and portfolio constraints and full…
The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only…
Volatility, as a primary indicator of financial risk, forms the foundation of classical frameworks such as Markowitz's Portfolio Theory and the Efficient Market Hypothesis (EMH). However, its conventional use rests on assumptions-most…
We consider the problem of active portfolio management, where an investor seeks the portfolio with maximal expected utility of the difference between the terminal wealth of their strategy and a proportion of the benchmark's, subject to a…
We construct a correlation matrix based financial network for a set of New York Stock Exchange (NYSE) traded stocks with stocks corresponding to nodes and the links between them added one after the other, according to the strength of the…