Optimizes portfolios using CPT utility via convex optimization.
problem Maximizing CPT utility in portfolio selection.
method Minorization-maximization (MM) algorithm and convex-concave (CC) procedure.
result Problems can be solved globally and efficiently.
Develops a new method for optimizing portfolios in stochastic markets.
problem Optimizing functionally generated portfolios in stochastic portfolio theory.
method Optimizes over a family of rank-based portfolios parameterized by an exponentially concave function.
result Proves existence and uniqueness of the optimization problem and provides stability estimates.
Study optimal portfolio choice with risk control for log-returns.
problem Optimal portfolio choice with risk management in continuous-time markets.
method Characterized optimal terminal wealth using concave envelope, derived analytical expressions for optimal wealth and policy, found efficient frontier.
result Efficient frontier is concave curve connecting minimum-risk to growth-optimal portfolios, not a vertical line.
In stochastic portfolio theory, a relative arbitrage is an equity portfolio which is guaranteed to outperform a benchmark portfolio over a finite horizon. When the market is diverse and sufficiently volatile, and the benchmark is the market or a buy-and-hold portfolio, functionally generated portfolios introduced by Fe…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave functions on the unit simplex measure the concentration of capital, and their gr…
Study optimizes growth rate for investors with long-only constraints.
problem Maximizing growth rate under drift uncertainty and long-only constraints.
method Developed a finite dimensional approximation for concave functionally generated portfolios.
result Proved uniqueness and existence for optimal portfolios under long-only constraints.
We treat a discrete-time asset allocation problem in an arbitrage-free, generically incomplete financial market, where the investor has a possibly non-concave utility function and wealth is restricted to remain non-negative. Under easily verifiable conditions, we establish the existence of optimal portfolios.
Optimizes investment under uncertain time horizons with non-concave utility.
problem Optimizing investment decisions with non-concave utility and uncertain time horizons.
method Established necessary and sufficient conditions for optimality, suggested recursive procedure for non-concave utility.
result Optimal investment strategies under uncertain time horizons exhibit multimodal distribution, indicating flexibility in switching between local maximizers.
The study bounds the utility of empirically optimal portfolios using stock return data.
problem Maximizing expected ratio of portfolio utility to best asset utility.
method High probability utility bounds derived from Lipschitz or Hölder continuous utility functions.
result Utility bounds depend on utility function, number of assets, and observations.
The paper analyzes portfolio selection with non-concave utility and transaction costs.
problem Non-concave utility maximization with proportional transaction costs.
method Two-step procedure: asymptotic terminal behavior analysis and discontinuous viscosity solution.
result Optimal portfolio strategies can differ significantly from the frictionless case due to transaction costs.
First introduced by Fernholz in stochastic portfolio theory, functionally generated portfolio allows its investment performance to be attributed to directly observable and easily interpretable market quantities. In previous works we showed that Fernholz's multiplicatively generated portfolio has deep connections with o…
Optimal portfolios are found for a wide range of utility functions under hyperbolic returns.
problem Portfolio optimization under expected utility criterion for large portfolios.
method Analytical expressions for optimal portfolios under hyperbolic return distributions and various utility functions.
result The two-fund separation holds true for a broad class of utility functions.
A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper we showed that gradient maps of exponentially concave functions provide solutions to a Monge-Kantorovich optimal transport problem and give a better gradient approximat…
We consider the terminal wealth utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a convex function g of the terminal wealth. The manager's own utility function U is assumed to be smooth and strictly concave, however the resulting utilit…
Investigates portfolio selection with transaction costs and stochastic volatility, using deep learning for computation.
problem Optimal portfolio selection with transaction costs and stochastic volatility.
method Two-factor stochastic volatility model, option-implied utility function, deep learning policy iteration.
result Deep learning method effectively computes optimal investment decisions under transaction costs and stochastic volatility.
We solve S-shaped utility portfolio selection with SD constraints using algorithms and neural networks.
problem Optimizing portfolios with S-shaped utility functions under SD constraints.
method First-order SD constraint solution, numerical algorithm for SSD, neural network approach.
result Effective numerical and neural network solutions for SSD constrained problems.
Novel framework for portfolio selection considering utility and risk.
problem Maximizing utility subject to risk constraints with various utility and risk functionals.
method General framework accommodating non-concave utilities and non-convex risk measures. Characterization of well-posedness using a simple either-or criterion.
result Minimal condition for well-posedness: either utility or risk must be sensitive to large losses.
We consider non-concave and non-smooth random utility functions with do- main of definition equal to the non-negative half-line. We use a dynamic pro- gramming framework together with measurable selection arguments to establish both the no-arbitrage condition characterization and the existence of an optimal portfolio i…
Investigates how rebalancing frequency and transaction costs affect log-optimal portfolios.
problem Impact of rebalancing frequency and transaction costs on log-optimal portfolios.
method Proved equivalence to concave program, derived optimality conditions, tested using intraday and daily data.
result Transaction costs can cause bankruptcy for frequency-dependent log-optimal portfolios, approximating to quadratic concave program.
Optimal portfolios are formed by combining momentum, size, and volatility characteristics, enhancing utility for all investors.
problem Estimation error in forming optimal portfolios from characteristics.
method Maximizing an in-sample loss function that is more concave than the utility function, linking weights to characteristics.
result Optimal portfolios with significantly higher certainty equivalents than benchmarks for all investors.
We analyze a nonlinear equation proposed by F. Black (1968) for the optimal portfolio function in a log-normal model. We cast it in terms of the risk tolerance function and provide, for general utility functions, existence, uniqueness and regularity results, and we also examine various monotonicity, concavity/convexity…
The overarching goal of this paper is to derive excess risk bounds for learning from exp-concave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, a…
Optimizes bond portfolios to avoid worst-case losses.
problem Finding the worst-case value of a bond portfolio over a range of yield curves and spreads.
method Solves a convex-concave saddle point optimization problem to find the worst-case value and construct a robust portfolio.
result Constructs a bond portfolio that includes the worst-case value, ensuring robustness against market uncertainties.
Study nonconcave portfolio choice with smooth ambiguity and Bayesian learning.
problem Nonconcave portfolio choice under smooth ambiguity and Bayesian learning.
method Developed a general framework for dynamic, non-concave asset allocation.
result Dynamic consistency achieved through a robust representation.
The paper studies price impacts in asset liquidation markets.
problem Understanding price impacts in asset liquidation markets.
method Equilibrium formulation and analysis of price impacts.
result Existence and uniqueness of clearing prices for portfolio liquidation.
A scalable gradient-based framework for sparse portfolio selection.
problem Sparse minimum-variance portfolio selection with cardinality constraint.
method Gradient-based optimization with Boolean relaxation and tunable parameter.
result Matches commercial solvers in most instances, differing by a few assets with negligible error in portfolio variance.
Functional portfolio generation, initiated by E.R. Fernholz almost twenty years ago, is a methodology for constructing trading strategies with controlled behavior. It is based on very weak and descriptive assumptions on the covariation structure of the underlying market model, and needs no estimation of model parameter…
Efficiently solves large-scale robust portfolio optimization problems.
problem High computational demands in large-scale robust portfolio optimization.
method Extended supporting hyperplane approximation for distributionally robust portfolio problems.
result Significantly reduces computational time from several thousand seconds to just a few.
Paper examines costs of using wrong price impact models in trading.
problem Misspecifying price impact models in trading predictions.
method Derives formulas for misspecification costs and applies to trading data.
result Misspecification costs are asymmetric, affecting profits and losses.
Method constructs CFMMs matching desired payoffs.
problem Creating CFMMs with specific payoff functions.
method Uses convex analysis and Fenchel conjugacy.
result Every concave, nonnegative, nondecreasing, 1-homogeneous payoff has a corresponding convex CFMM.
New method finds arbitrage opportunities in fluctuating asset bands.
problem Finding arbitrage opportunities in fluctuating asset bands.
method Formulate as maximizing volatility within a price band, using convex-concave optimization.
result Approximately solves non-convex optimization problem for moving-band arbitrage.
Study optimal control strategy for hedge funds managers with PSAHARA utility family.
problem Optimizing risk and reward in incomplete markets with non-monotone risk aversion and convex compensation.
method Introduced PSAHARA utility family to model non-monotone risk aversion and convex compensation. Proved concavification techniques for non-concave utility functions. Derived explicit optimal control strategy.
result PSAHARA utility induces risk-taking behavior even with convex compensation, leading to high returns and volatility.
Algorithm finds near-optimal VaR portfolios using MILP, improving risk management.
problem Computing optimal VaR portfolios is hard due to non-convexity and combinatorial nature.
method Formulates VaR portfolio problem as MILP, uses alternate formulations for guarantees.
result Near-optimal VaR portfolios with near-optimality guarantees.
Geometric framework for CFMMs simplifies many results.
problem Understanding the behavior of CFMMs without strong conditions.
method Developed a geometric framework encompassing known results.
result CFMMs have a canonical trading function with specific properties.
We consider the following problem in stochastic portfolio theory. Are there portfolios that are relative arbitrages with respect to the market portfolio over very short periods of time under realistic assumptions? We answer a slightly relaxed question affirmative in the following high dimensional sense, where dimension…
We maximize the expected utility of terminal wealth in an incomplete market where there are cone constraints on the investor's portfolio process and the utility function is not assumed to be strictly concave or differentiable. We establish the existence of the optimal solutions to the primal and dual problems and their…
Unified formula for optimal portfolio under piecewise hyperbolic risk aversion.
problem Optimizing portfolios with piecewise hyperbolic risk aversion utilities.
method Derive a unified closed-form formula for the optimal portfolio.
result Unified formula reflects risk aversion behaviors and risk-taking behaviors.
We explain a general construction through which concave elliptic operators on complex manifolds give rise to concave functions on cohomology. In particular, this leads to generalized versions of the Khovanskii-Teissier inequalities.
We show that some specific market risk measures implied by current international capital regulation (the Basel Accords and the Capital Adequacy Directive of the European Union) violate the obvious requirement of convexity in some regions in the space of portfolio weights.
This paper tackles robust control of noisy systems with uncertain distributions.
problem Optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity.
method Develops a convex relaxation to handle the ``concave-max'' geometry and derives a probabilistic performance guarantee.
result Derives an explicit, non-asymptotic bound on the duality gap and proves robust viability conditions.
The paper establishes conditions for strict power concavity in convolutions.
problem Conditions for strict power concavity in convolutions.
method Analyzes sufficient conditions for strict parabolic power concavity of convolutions.
result Establishes sufficient conditions for strict power concavity of convolutions.
The paper examines how background risk affects portfolio selection and optimal reinsurance design.
problem Maximizing the probability of reaching a financial goal in the presence of background risk.
method Quantile formulation method to derive optimal solutions explicitly.
result The presence of background risk does not change the solution shape but alters the parameter values.
Develops deep learning methods for solving S-shaped utility maximisation problems.
problem Optimizing portfolios with S-shaped utility and random benchmarks.
method Uses deep learning and duality methods to solve the Hamilton-Jacobi-Bellman equation and adjoint equation.
result Demonstrates the accuracy of deep learning methods for non-concave utility maximisation problems.
In this paper we continue the study of Bian-Miao-Zheng (2011) and extend the results there to a more general class of utility functions which may be bounded and non-strictly-concave and show that there is a classical solution to the HJB equation with the dual control method. We then apply the results to study the effic…
In this paper, we propose a novel investment strategy for portfolio optimization problems. The proposed strategy maximizes the expected portfolio value bounded within a targeted range, composed of a conservative lower target representing a need for capital protection and a desired upper target representing an investmen…
The choice of admissible trading strategies in mathematical modelling of financial markets is a delicate issue, going back to Harrison and Kreps (1979). In the context of optimal portfolio selection with expected utility preferences this question has been a focus of considerable attention over the last twenty years. We…
We present a simple connection between differential Harnack inequalities for hypersurface flows and natural concavity properties of their time-of-arrival functions. We prove these concavity properties directly for a large class of flows by applying a concavity maximum principle argument to the corresponding level set f…
Introduces new weighted floating functions and affine surface areas.
problem Developing new mathematical concepts for convex bodies.
method Introducing weighted floating functions and weighted functional affine surface areas.
result New relations to traditional and classical affine surface areas.