Investigates portfolio selection for rank-dependent utilities in incomplete markets.
problem Portfolio selection for agents with rank-dependent utility in incomplete financial markets.
method Characterizes deterministic strict equilibrium strategies for constant-coefficient and time-invariant probability weighting functions. Addresses the issue of selecting an optimal strategy from multiple equilibrium strategies for time-variant probability weighting functions.
result Characterizes deterministic strict equilibrium strategies and identifies optimal strategies from multiple equilibrium strategies.
Proposes a robust equilibrium strategy for mean-variance portfolio selection.
problem Time-inconsistency in mean-variance portfolio selection.
method Introduces a novel definition of robust equilibrium strategy and solves the corresponding PDE system.
result A classical solution to the PDE system implies a robust equilibrium strategy.
The paper solves a portfolio selection problem in incomplete markets by balancing utility and risk.
problem Time-inconsistent portfolio selection in incomplete markets.
method Characterizes equilibrium via a coupled quadratic BSDE system, introduces approximate equilibrium for general cases.
result Established existence theory for equilibrium strategies in special and general cases.
The paper solves stochastic control problems with implicit objectives, finding equilibrium strategies.
problem Stochastic control problems with implicitly defined objectives leading to time-inconsistency.
method Closed-loop equilibrium solutions in a controlled diffusion framework, providing sufficient and necessary conditions.
result Explicit characterization of equilibrium portfolio strategies in terms of ordinary differential equations.
Investigates time-inconsistent portfolio selection under MMV preferences.
problem Time-inconsistent optimal strategies for MMV preferences.
method Nash equilibrium controls for MMV and MV preferences, solving FBSDE and HJB equations.
result MMV optimal strategies lead to higher investment amounts than MV strategies, narrowing over time.
The paper explores how investors make decisions under disappointment aversion, finding that they prefer not to invest.
problem Continuous-time portfolio selection under generalized disappointment aversion.
method Sufficient and necessary condition for equilibrium strategies via fully nonlinear integral equation.
result Equilibrium strategy under disappointment aversion leads to less investment in the stock market compared to classical utility theory.
In this paper, we solve the time inconsistent portfolio selection problem by using different utility functions with a moving target as our constraint. We solve this problem by finding an equilibrium control under the given definition as our optimal control. We firstly derive a sufficient equilibrium condition for secon…
The paper solves portfolio selection for complex preferences in continuous time.
problem Dynamic portfolio selection for nonlinear preferences with time inconsistency.
method Stochastic maximum principle and verification theorems for equilibrium strategies.
result Equilibrium strategies derived in closed form for CRRA and CARA preferences.
Paper characterizes equilibrium strategies for stochastic control with higher-order moments.
problem Stochastic control problems with higher-order moments.
method Novel characterization of time-consistent control problems, deriving equilibrium conditions via BSDEs.
result Derives sufficient and necessary conditions for an open-loop Nash equilibrium control (ONEC) in a novel way.
The study finds that maximizing median returns is the only viable strategy in portfolio selection.
problem Difficulties in studying optimal portfolio strategies due to discontinuity and time inconsistency in maximizing median and quantile returns.
method Used intra-personal equilibrium approach to analyze portfolio selection under median and quantile maximization.
result Median maximization is the only viable strategy, with no investment in risky assets for other quantiles.
The paper characterizes equilibrium strategies under random risk aversion, showing unique solutions based on risk aversion distribution.
problem Characterizing equilibrium strategies in a continuous-time portfolio selection problem under random risk aversion.
method Provided a complete characterization of all deterministic equilibrium strategies in closed form, analyzing the structure of the solution based on the distribution of random risk aversion.
result The equilibrium is unique (if exists) when the expectation of random risk aversion is finite, but infinite expectation leads to either infinitely many equilibria or a unique trivial one.
The paper analyzes how investors' wealth can decline collectively under partial information.
problem Investors' wealth can decline collectively under partial information.
method The paper derives a Nash equilibrium for mean-variance portfolio selection under relative performance criteria, considering both full and partial information.
result Relative performance criteria can lead to downward self-reinforcement of investors' wealth, which is more pronounced under partial information.
Investor selects portfolios based on news attention in a hidden Markov model.
problem Mean-variance portfolio selection in a dynamic attention context.
method Closed-loop equilibrium strategies via extended HJB equation and Markov chain approximation.
result Equilibrium strategies found through iterative algorithm and numerical examples.
Proposes a new criterion for selecting Nash equilibria considering both utility and inequality.
problem Finding a fair Nash equilibrium in group decision-making.
method Introduces entropy-norm space for geometric selection of strict Nash equilibria.
result The closest entropy-norm pair to the largest entropy-norm pair in rescaled space is the most suitable equilibrium.
A Systemic Optimal Risk Transfer Equilibrium (SORTE) was introduced in: "Systemic optimal risk transfer equilibrium", Mathematics and Financial Economics (2021), for the analysis of the equilibrium among financial institutions or in insurance-reinsurance markets. A SORTE conjugates the classical Bühlmann's notion of a …
We present a simple dynamic equilibrium model for an online exchange where both buyers and sellers arrive according to a exogenously defined stochastic process. The structure of this exchange is motivated by the limit order book mechanism used in stock markets. Both buyers and sellers are elastic in the price-quantity …
Investigates portfolio selection among competitive agents with mean-variance preferences.
problem Optimizing portfolios with multi-agent competition and relative wealth comparison.
method Reformulated as a constrained, non-homogeneous stochastic linear-quadratic control problem; derived optimal feedback strategies; used decoupling techniques and fixed-point theory to solve nonlinear BSDEs.
result Characterized three scenarios based on market and competition parameters: unique Nash equilibrium, no Nash equilibrium, or infinitely many Nash equilibria.
Intuitive clustering algorithm balances cluster size and cohesion.
problem Cluster definition and selection in data analysis.
method Nearest neighbours equilibrium condition for clustering.
result High-quality clustering solutions compared to benchmarks.
Naive investors make riskier choices than optimal strategies in continuous-time finance.
problem Continuous-time Markowitz portfolio selection with naive reoptimization.
method Analytical derivation of naive policies from discretely naive policies.
result Naive policies are always riskier and less efficient than equilibrium policies.
In this paper, we continue our study on a general time-inconsistent stochastic linear--quadratic (LQ) control problem originally formulated in [6]. We derive a necessary and sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional…
In this paper, we consider equilibrium strategies under Volterra processes and time-inconsistent preferences embracing mean-variance portfolio selection (MVP). Using a functional Itô calculus approach, we overcome the non-Markovian and non-semimartingale difficulty in Volterra processes. The equilibrium strategy is the…
New CGMD model predicts non-equilibrium processes better than existing methods.
problem Inconsistency in conditional distribution of unresolved variables.
method Time-lagged independent component analysis to minimize entropy contribution of unresolved variables.
result The model's generalization ability for non-equilibrium processes is significantly improved.
Study optimal investment-reinsurance strategies in equity-linked insurance products using Stackelberg game theory.
problem Optimizing investment and reinsurance strategies in equity-linked insurance products with capital guarantees.
method Modelled as a Stackelberg game where reinsurer acts as leader and insurer as follower, with general utility functions and power utility functions analyzed.
result Derive Stackelberg equilibrium for general utility functions and calculate it explicitly for power utility functions, finding reinsurer optimizes premium to incentivize maximal reinsurance purchase.
In this paper, we formulate a general time-inconsistent stochastic linear--quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution withi…
New findings show strategic interactions can undermine model expressiveness in machine learning.
problem How strategic interactions affect model performance in machine learning.
method Analyzing model expressiveness and strategic interactions in various machine learning settings.
result Optimizing over less expressive model classes can lead to better equilibrium outcomes in strategic environments.
The paper analyzes a game where players must balance short-term and long-term interests, leading to cooperative or competitive outcomes.
problem Analyzing time inconsistency in inter-personal decision-making under non-exponential discounting.
method Iterative procedures and Zorn's lemma to find Nash equilibria between players' intra-personal equilibria.
result Inter-personal equilibria exist and depend on the impatience levels of the players.
The topology and the geometry of a surface play a fundamental role in determining the equilibrium configurations of thin films of liquid crystals. We propose here a theoretical analysis of a recently introduced surface Frank energy, in the case of two-dimensional nematic liquid crystals coating a toroidal particle. Our…
Study liquidity provision in decentralized exchanges considering risk aversion and replication costs.
problem Economic viability of liquidity provision in decentralized exchanges (DEXs).
method Formulated strategic interactions as a sequential game with risk-averse LP, traders, and arbitrageurs.
result DEX liquidity depth is crucial for risk management, influenced by risk aversion and replication costs.
Modeling gas fee competition in decentralized exchanges to optimize arbitrage profits.
problem Gas fees and transaction ordering in decentralized exchanges create arbitrage opportunities.
method Developed a first equilibrium model of gas fee competition between two arbitrageurs under three transaction reversion settings.
result Mixed equilibria exist, and their characteristics depend on inventory risk and transaction settings.
Optimizes long-term social welfare in recommender systems by matching users to providers.
problem Realistic recommender systems dynamics affect all agents, not just users.
method Formulated as an optimal constrained matching problem, solved using dynamical system equilibrium selection.
result Ensures maximal social welfare with diverse viable providers, improving over myopic matching.
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.
Study efficient offline RL in Markov games with general models.
problem Learn approximate equilibria from offline data in Markov games.
method Use Bellman-consistent pessimism for interval estimation and optimize gap relaxation.
result First framework for sample-efficient offline learning in Markov games, handling all equilibria.
An interesting toy model has recently been proposed on Schumpeterian economic dynamics by Thurner {\it et al.} following the idea of economist Joseph Schumpeter. Punctuated equilibrium dynamics is shown to emerge from this model and some detail analyses of the time series indicate SOC kind of behaviours. The focus in t…
REMAL: Residual Equilibrium Manifold Active Learning for Surrogate-Based Multidisciplinary Design Analysis
problem Multidisciplinary design analysis of coupled engineering systems requires solving equilibrium states where all disciplinary coupling variables are consistent.
method Residual manifold surrogate modeling framework for coupled systems.
result REMAL learns a surrogate model of the joint residual manifold via multitask Gaussian process models.
Study optimal portfolios for many players in a market model with random coefficients.
problem Optimal portfolio selection for many players under relative performance criteria in a market model with random coefficients.
method Game theory and stochastic optimal control, focusing on CARA and CRRA risk preferences, and extending to continuum of players.
result Existence of forward Nash equilibrium and mean field equilibrium for the n-agent game and corresponding mean field stochastic optimal control problem.
In this article, we present a discrete time modeling framework, in which the shape and dynamics of a Limit Order Book (LOB) arise endogenously from an equilibrium between multiple market participants (agents). We use the proposed modeling framework to analyze the effects of trading frequency on market liquidity in a ve…
Investors with asymmetric information play a game to optimize their portfolios.
problem Two investors with different information levels compete in portfolio selection.
method Modelled as a Stackelberg game with entropy-regularized mean-variance objectives.
result Equilibria exist where follower's strategy depends on leader's actions.
Investment strategies for rank-dependent utility agents are derived in a continuous-time market.
problem Time inconsistency in rank-dependent utility models.
method Study of consistent planners seeking intra-personal equilibrium strategies.
result Explicit final wealth profile replicating equilibrium strategies, with scaling function derived.
Brokers and an informed trader compete for liquidity, affecting trading costs and inventory risk.
problem How brokers and an informed trader manage liquidity and trading costs.
method Sequential Stackelberg game, solving for trading strategies, numerical solutions.
result Equilibrium strategies and liquidity prices determined, not Pareto efficient.
Study Nash competition among dealers quoting prices to clients with unknown trading motives.
problem Adverse selection and inventory costs in dealer-client interactions.
method Analyzes one-shot Nash competition with unknown client type and inventory constraints.
result Unique symmetric Nash equilibrium exists and can be characterized by a nonlinear ODE.
Study proposes new OPE estimators for two-player zero-sum games.
problem Evaluating new policies using historical data from a different policy in multi-player zero-sum games.
method Doubly robust and double reinforcement learning estimators to project exploitability.
result Prove exploitability estimation error bounds and regret bounds for policy profiles.
Study on optimal trading in a finite population with market frictions and asymmetric information.
problem Optimal trading in a finite population with market frictions and asymmetric information.
method Investigates stochastic differential games with asymmetric information and market frictions, proving existence and uniqueness of Nash and Stackelberg-Nash equilibria.
result Existence and uniqueness of Nash and Stackelberg-Nash equilibria in both unconstrained and constrained trading scenarios.
Efficient algorithm converges to Nash equilibrium in bilinear problems with bandit feedback.
problem Learning dynamics in bilinear saddle-point problems with bandit feedback.
method Uncoupled learning algorithm combining experimental design and FTRL with a tailored regularizer.
result Last-iterate convergence rate of ildeO(T−1/4) in high probability. On curved spaces, viscous fluids reach equilibrium quickly.
problem Thermalization of viscous fluids on negatively curved manifolds.
method Stochastic Navier-Stokes equations with kinematically selected deformation Laplacian.
result Exponential thermalization rate of $2νλ_\Def$.
Study high-frequency trading game with price impact, finding unique equilibrium.
problem Optimal execution in a trading game with transient price impact.
method Analyzes high-frequency limit of an n-trader optimal execution game. result High-frequency limit converges to a continuous-time model with quadratic costs.
Study on investment strategy for agents with periodic preferences and discounting.
problem Investment decisions by agents with periodic S-shaped preferences and present bias.
method Infinite-horizon, continuous-time portfolio selection problem with quasi-hyperbolic discounting.
result Time-consistent planning strategy can be formulated as an equilibrium to a static mean field game.
A \emph{new} notion of equilibrium, which we call \emph{strong equilibrium}, is introduced for time-inconsistent stopping problems in continuous time. Compared to the existing notions introduced in ArXiv: 1502.03998 and ArXiv: 1709.05181, which in this paper are called \emph{mild equilibrium} and \emph{weak equilibrium…
We study the market selection hypothesis in complete financial markets, populated by heterogeneous agents. We allow for a rich structure of heterogeneity: individuals may differ in their beliefs concerning the economy, information and learning mechanism, risk aversion, impatience and 'catching up with Joneses' preferen…