Study of portfolio management under relative performance concerns using mean field games.
problem Portfolio management problems under relative performance concerns.
method Forward utilities of CARA type, mean field games, best response and equilibrium strategies.
result Solve forward-utility finite player game and mean-field game under asset specialization.
Proves weak convergence equals mean convergence in GGC.
problem Proving convergence in GGC distributions.
method Using generalized gamma convolution (GGC) and expected utility maximization.
result Weak convergence implies mean convergence in GGC.
The paper characterizes optimal dynamic portfolios for a modified mean-variance utility.
problem Optimal dynamic portfolio choice for a modified mean-variance utility.
method Complete characterization under minimal assumptions, no restrictions on asset return moments.
result Maximal MMV utility is linked to the monotone Sharpe ratio, with global squared MSR as the nominal yield.
New optimal portfolios derived for power and logarithmic utilities under log-normal returns.
problem Optimal portfolio weights for power and logarithmic utilities under log-normal returns.
method Closed-form expressions derived for optimal portfolio weights, proving mean-variance efficiency.
result Both optimal portfolios are mean-variance efficient and belong to the feasible set.
New optimization method for portfolio management maximizing wealth and utility with risk control.
problem Maximizing terminal wealth and utility with mean-variance risk control.
method Transformed into a single-objective problem using overall happiness, solved in game theoretic framework.
result Closed-form solutions for specific utility functions reveal new optimal investment strategies.
Study optimal investment strategies for competitive agents using Mean Field Games.
problem Optimizing portfolios with relative performance criteria.
method Mean Field Game framework applied to CRRA and CARA utility cases.
result Derivation of optimal investment and consumption strategies.
Study solves wealth maximization problem with unbounded mean and volatility.
problem Maximizing terminal wealth with unbounded mean and volatility under Knightian uncertainty.
method Solves utility maximization problem explicitly with Ornstein-Uhlenbeck and GARCH(1) processes.
result First work on unbounded mean and volatility with Knightian uncertainty and nondominated priors.
Study on price formation among investors with exponential utility and liabilities.
problem Equilibrium price formation among investors with heterogeneous risk-averseness and liabilities.
method Mean-field game theory and mean-field backward stochastic differential equations (BSDE).
result Existence of equilibrium risk-premium process and market clearing in the large population limit.
In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimiz…
Study of a game with multiple players and common shocks using probabilistic methods.
problem Analyze a game with multiple players and common shocks.
method Probabilistic approach to study the game, including mean field and FBSDEs.
result Unique equilibrium found for both N-player and mean field games.
Solves optimal control for trading multiple mean-reverting assets.
problem How to construct a portfolio from mean-reverting assets.
method Optimal control problem for power utility agent.
result Nearly explicit solution with properties of optimal solution.
The paper solves an insurance problem using mean-variance and rank-dependent utility theory.
problem Formulating and solving an insurance problem with rank-dependent utility and mean-variance premium principle.
method Formulated as a non-concave maximization problem, then turned into a concave quantile optimization problem, solved using calculus of variations.
result An optimal insurance contract is derived and numerically computed.
We review the utility-based valuation method for pricing derivative securities in incomplete markets. In particular, we review the practical approach to the utility-based pricing by the means of computing the first order expansion of marginal utility-based prices with respect to a small number of random endowments.
New model considers wealth and time affecting risk aversion in portfolio selection.
problem Optimal investment strategy and consumption process depend on wealth and future income balance.
method Proposed a new mean-variance-utility framework with time and state-dependent risk aversion, solved using game theory.
result Equilibrium investment and consumption policies derived, aligning with investor behavior.
The paper optimizes portfolios with few assets under uncertainty.
problem Optimizing portfolios with many assets under uncertain returns.
method Penalized utility approach for selecting a sparse set of optimal weights.
result Produces a small, sparsified portfolio from many assets.
The Mean-Variance Criterion is equivalent to Second-order Stochastic Dominance under symmetric Elliptical distributions.
problem Determining the equivalence of Mean-Variance Criterion and Stochastic Dominance Criteria.
method Analyzing under symmetric and Skew-Elliptical distributions using Monte Carlo simulations.
result The Mean-Variance Criterion does not coincide with Second-order Stochastic Dominance for some types of risk-averse investors.
Closed-form optimal portfolios for exponential utility in small/large markets.
problem Optimal portfolios maximizing exponential utility in small/large financial markets.
method Closed-form expressions for optimal portfolios in small markets, convergence to large market optimal utility, numerical procedure for general utility functions.
result Optimal utility in large markets converges to optimal utility in small markets, requiring infinite diversification.
Theory integrates loss aversion into expected utility for monetary returns.
problem Modeling loss aversion in expected utility theory.
method Develops state-dependent linear utility functions incorporating loss aversion.
result Contracts from monopolists in insurance markets.
The paper analyzes optimal timing to sell assets under different price dynamics and utility functions.
problem Optimal timing to sell risky assets under different price dynamics and risk preferences.
method Two stochastic models (trending and mean-reverting) and three utility functions (exponential, power, log) are considered to derive optimal thresholds and certainty equivalents.
result The timing option can make the investor's value function and certainty equivalent non-concave in price.
Introduces RPU to explain randomization preference in dynamic settings.
problem Explains preference for randomization in dynamic investment problems.
method Introduces recursive perturbed utility (RPU) to incorporate randomization preference.
result Proves RPU-optimal portfolio policy is Gaussian and can be expressed in closed form.
Optimizes portfolios with utility theory, diversification, and leverage.
problem Finding optimal portfolio allocation strategies.
method Utility theory, exponential and logarithmic utilities, compound probability distributions, maximum expected utility, generalized mean-variance.
result Enhanced portfolio allocation strategies with natural explanations.
The paper solves a dynamic portfolio optimization problem using Riccati transformation.
problem Dynamic stochastic portfolio optimization involving expected and intertemporal utilities.
method Solving a fully nonlinear HJB equation through Riccati transformation into a quasi-linear parabolic equation.
result The numerical method based on semi-implicit scheme converges at second order.
Study Epstein-Zin preferences in mean field portfolio games, proving unique equilibria.
problem Analyzing portfolio games with Epstein-Zin preferences under non-Markovian conditions.
method Proves a one-to-one correspondence between Nash equilibria and BSDE solutions, using local stochastic maximum principle tailored to Epstein-Zin utility.
result Establishes uniqueness of equilibria in mean field portfolio games under Epstein-Zin preferences.
FCA improves fair clustering by optimizing utility and fairness.
problem Balancing fairness and utility in clustering.
method FCA alternates between aligning data and optimizing cluster centers in an aligned space.
result FCA achieves a superior trade-off between fairness and utility.
Study Nash equilibria for risk-averse investors in a market with transient price impact.
problem Optimizing costs or maximizing expected utility for risk-averse agents in a market with transient price impact.
method Explicit representations and numerical analysis of Nash equilibria for mean-variance optimization and expected exponential utility maximization.
result Explicit representations and uniqueness of Nash equilibria for mean-variance optimization.
The paper studies the robust maximization of utility of terminal wealth in the diffusion financial market model. The underlying model consists with risky tradable asset, whose price is described by diffusion process with misspecified trend and volatility coefficients, and non-tradable asset with a known parameter. The …
Study optimal investment and consumption strategies for competitive agents with habit formation.
problem Optimal investment and consumption strategies for competitive agents with habit formation.
method Formulated n-agent game problems and mean field game problems, derived mean field equilibrium, constructed approximate Nash equilibrium.
result Explicit convergence order of approximate Nash equilibrium can be obtained.
The study proves a theorem for surfaces using Codazzi operators and investigates parallel mean curvature surfaces.
problem Understanding surfaces with parallel mean curvature in product spaces.
method Intrinsic Klotz-Osserman theorem and Simons' formula.
result The existence of surfaces with parallel mean curvature in product spaces with non-positive Gaussian curvature.
Study analyzes investment strategies for fund managers competing in a common market.
problem Optimal investment strategies for fund managers competing in a common market with relative performance criteria.
method Construct explicit constant equilibrium strategies for both finite population games and mean field games.
result Explicit strategies show how competition affects investment behavior in risky assets.
New results on financial equilibria in markets with general semimartingales.
problem Existence and uniqueness of mean-variance equilibria in semimartingale markets.
method Analysis of dynamic mean-variance hedging and fixed-point problems.
result First results allowing for general semimartingales and both discrete and continuous time.
Develops asset pricing models with mean field game theory for heterogeneous agents.
problem Tackles equilibrium asset pricing in incomplete markets with heterogeneous agents.
method Uses mean field game theory and mean field backward stochastic differential equations (BSDEs).
result Derives equilibrium risk premium and shows market clearing in the large population limit.
The paper addresses portfolio allocation with uncertain covariance matrices, finding a logarithmic risk dependence.
problem Portfolio allocation with uncertain covariance matrices.
method Calculates the expected value of CARA utility function over a distribution of covariance matrices, considering uncertainty in future returns and covariances.
result Marginalization introduces a logarithmic dependence on risk, leading to lower allocation levels for higher uncertainties.
The paper examines utility maximization in markets with hidden Gaussian drift, finding restrictions on model parameters.
problem Utility maximization problems in markets with hidden Gaussian drift mean-reverting processes.
method Derives sufficient conditions for bounded maximum expected utility of terminal wealth for models with full and partial information.
result Restrictions on model parameters for bounded maximum expected utility.
The paper introduces new portfolio rules beyond mean-variance, addressing asymmetry and uncertainty.
problem Optimizing portfolios with asymmetric returns and uncertainty in expected returns.
method Derives allocation rules for asymmetric Laplace distributed returns and random normal expected returns. Addresses singular covariance matrices and uncertainty in returns.
result Optimal worst-case scenario solution provides a convex alternative to risk parity, improving portfolio stability.
A method for low-dimensional MDP representation using deep neural networks.
problem Constructing a low-dimensional Markov decision process representation.
method Use a deep neural network to define a class of potential process representations and estimate the process of lowest dimension.
result A decision strategy that maximizes mean utility for the low-dimensional representation also maximizes mean utility for the original process.
The model of rational decision-making in most of economics and statistics is expected utility theory (EU) axiomatised by von Neumann and Morgenstern, Savage and others. This is less the case, however, in financial economics and mathematical finance, where investment decisions are commonly based on the methods of mean-v…
The paper confirms a conjecture about optimal expected utility in discrete-time markets approaching a continuous-time model.
problem Analyzing the convergence of optimal expected utility in discrete-time markets to a continuous-time model.
method Examined a sequence of discrete-time economies generated by scaled random walks, and compared their optimal expected utilities to the continuous-time Black-Scholes-Merton model.
result The conjecture holds for utility functions with asymptotic elasticity strictly less than one, but fails for elasticity equal to one.
Utilizing a weight matrix we study surfaces of prescribed weighted mean curvature which yield a natural generalisation to critical points of anisotropic surface energies. We first derive a differential equation for the normal of immersions with prescribed weighted mean curvature, generalising a result of Clarenz and vo…
Generalizes k-means to graphs using PageRank.
problem Clustering nodes in directed and undirected graphs.
method Utilizes PageRank to compute node centrality in graphs.
result Robustly computes centrality in graphs and metric spaces.
Kramkov and Sirbu (2006, 2007) have shown that first-order approximations of power utility-based prices and hedging strategies can be computed by solving a mean-variance hedging problem under a specific equivalent martingale measure and relative to a suitable numeraire. In order to avoid the introduction of an addition…
The paper optimizes portfolios in a market with hidden drift and random expert opinions.
problem Optimizing portfolios in a market with hidden Gaussian drift and random expert signals.
method Modeling the hidden drift using Kalman filters and solving the utility maximization problem with dynamic programming.
result Derivation of optimal portfolio weights and utility maximization under the given market conditions.
Extends differential privacy to Riemannian manifolds, improving utility.
problem Releasing private statistical summaries on Riemannian manifolds.
method Extended Laplace or K-norm mechanism using intrinsic distances and volumes.
result Demonstrates rate optimality and utility improvement over ambient spaces.
The paper analyzes optimal portfolio allocation under a fast mean-reverting fractional stochastic environment.
problem Optimal portfolio allocation under a fractional stochastic environment with long-range dependence.
method Analyzes the nonlinear optimal portfolio allocation problem using a stationary fractional Ornstein-Uhlenbeck process with fast mean-reverting.
result Establishes asymptotic optimality of zeroth order trading strategies and general utility functions within specific families of admissible strategies.
The paper confirms a conjecture about optimal expected utility in markets with insider information.
problem Optimal expected utility in markets with insider information.
method An extension of the Black-Scholes-Merton model with a sequence of discrete-time economies.
result Optimal expected utility converges to the classic model when conditions are met.
Modern portfolio theory(MPT) addresses the problem of determining the optimum allocation of investment resources among a set of candidate assets. In the original mean-variance approach of Markowitz, volatility is taken as a proxy for risk, conflating uncertainty with risk. There have been many subsequent attempts to al…
The paper optimizes dynamic portfolios using utility maximization and risk measures.
problem Maximizing expected utility in dynamic stochastic portfolio optimization.
method Solves a dynamic stochastic portfolio optimization problem numerically using evolutionary Hamilton-Jacobi-Bellman equations and Riccati transformations.
result Defines and computes the Conditional Value-at-Risk deviation (CVaRD) based Sharpe ratio for risk-adjusted performance.
Model shows how centralization occurs in cryptocurrency mining.
problem Centralization of reward and computational power in Bitcoin-like cryptocurrencies.
method Mean field game model to study miner competition and reward distribution.
result Heterogeneity of initial wealth leads to greater imbalance in reward distribution.
Sharp curvature estimates for mean curvature flow in spheres.
problem Understanding the behavior of surfaces evolving under mean curvature flow in spheres.
method Proving asymptotically sharp curvature pinching estimates and using them to derive derivative and convexity estimates.
result Partial classification of singularity models and new rigidity results for ancient solutions.