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.
Study shows risk-averse investors have consistent ranking of risky assets.
problem Ranking of risky assets in short-term investments.
method Analyzes various decision problems regarding risky assets with continuous returns.
result Risk-averse decision makers have the same ranking over risky assets.
Optimizes information acquisition to reduce estimation risk and maximize utility.
problem Estimation risk in investor decision-making.
method Derives closed-form value functions using CARA and CRRA utility functions, employs variational methods to explore optimal acquisition.
result Acquiring information earlier is more valuable in reducing estimation risk and achieving higher utility.
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.
In this paper we provide an alternative framework to tackle the first-best Principal-Agent problem under CARA utilities. This framework leads to both a proof of existence and uniqueness of the solution to the Risk-Sharing problem under very general assumptions on the underlying contract space. Our analysis relies on an…
Investors' strategies in a market influenced by price impact are analyzed, showing aggressive behavior when impact exceeds a critical point.
problem Strategic interaction and Nash equilibria of investors in a financial market with price impact.
method Analysis of Nash equilibria for relative investors with CRRA and CARA utility functions in a Brownian motion-driven market, considering both linear and non-linear price impacts.
result Investors' aggressive behavior is observed when price impact exceeds a critical parameter.
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.
We analyze a family of portfolio management problems under relative performance criteria, for fund managers having CARA or CRRA utilities and trading in a common investment horizon in log-normal markets. We construct explicit constant equilibrium strategies for both the finite population games and the corresponding mea…
Study solves DREs for trading strategies using signals and past prices.
problem Solving DREs for optimal trading strategies.
method Analyzes DREs with indefinite matrix coefficients and applies to trading problems.
result Derives optimal trading strategies using signals and past prices.
This paper analyzes popular time-nonseparable utility functions that describe "habit formation" consumer preferences comparing current consumption with the time averaged past consumption of the same individual and "catching up with the Joneses" (CuJ) models comparing individual consumption with a cross-sectional averag…
This paper extends the classical consumption and portfolio rules model in continuous time (Merton 1969, 1971) to the framework of decision-makers with time-inconsistent preferences. The model is solved for different utility functions for both, naive and sophisticated agents, and the results are compared. In order to so…
Unified theory for optimal execution through signal-adaptive quotes in limit order books.
problem Optimal execution in limit order books with signal-dependent factors.
method Develops a unified solution theory for four execution criteria, incorporating signal-dependent drift, price impact, inventory risk, and execution risk.
result Explicit formulas reveal optimal quoting strategies and show signal-dependent drift can significantly affect execution.
This paper considers the optimal portfolio selection problem in a dynamic multi-period stochastic framework with regime switching. The risk preferences are of exponential (CARA) type with an absolute coefficient of risk aversion which changes with the regime. The market model is incomplete and there are two risky asset…
Investment strategy optimizes risk using a specific risk measure.
problem Optimizing investment with risk controlled by a weighted entropic risk measure.
method Investigation of expected utility maximization and risk minimization problems with solutions provided iteratively.
result Explicit characterization of solutions to optimization problems.
Investigates Meyer risk measures and their applications in finance.
problem Existence and structure of Meyer risk measures.
method Fractional stochastic dominance and Meyer's utility function.
result Existence and structure of risk measures respecting v-SD order. We solve the problem of optimal liquidation with volume weighted average price (VWAP) benchmark when the market impact is linear and transient. Our setting is indeed more general as it considers the case when the trading interval is not necessarily coincident with the benchmark interval: Implementation Shortfall and Ta…
Study time-inconsistent portfolio optimization for competitive agents with relative performance criteria.
problem Time-inconsistent mean field and n-agent games under relative performance criteria.
method Construct open-loop equilibrium strategies for n-agent games and mean field games.
result Explicit solutions for n-agent games and mean field games, unique in a special class of equilibria.
In this paper, we study an optimal excess-of-loss reinsurance and investment problem for an insurer in defaultable market. The insurer can buy reinsurance and invest in the following securities: a bank account, a risky asset with stochastic volatility and a defaultable corporate bond. We discuss the optimal investment …
Study optimal investment in large populations of competitive, heterogeneous agents.
problem Maximizing utility in a large, interacting agent system with relative performance concerns.
method Analyzes stochastic utility maximization game in finite and infinite agent settings, using graphon models and backward stochastic differential equations.
result Convergence of Nash equilibria and optimal utilities from finite to infinite agent models under specific conditions.
New framework for portfolio management using binomial markets and game theory.
problem Investment behavior in competitive and incomplete markets.
method Introduces PRFPP framework, constructs and analyzes for both finite and mean field games.
result Relative performance concerns do not always lead to more risky asset investment.
Study N-player and mean-field games in Itô-diffusion markets with competitive or homophilous interactions.
problem Optimal portfolio choice in a common market with N interacting players. method Analyzes N-player and mean-field games in incomplete and complete markets with CARA utilities and random risk tolerances. result Derives explicit or closed-form solutions for equilibrium processes and game values.
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.
This paper solves a financial portfolio selection problem in incomplete markets.
problem Portfolio selection in incomplete financial markets with ambiguity.
method Constructing an efficient frontier, simplifying the problem, introducing a new distorted Legendre transformation, and proving the bipolar relation and distorted duality theorem.
result The existence and uniqueness of optimal strategies are shown for different utility functions under specific conditions.
Forward hedging reshapes incentive provision in firms.
problem How does forward hedging affect incentive provision in firms?
method We consider a CARA framework to jointly characterize optimal production, compensation, and static hedging in equilibrium.
result Delegation and external hedging are partial substitutes, and delegation can increase firm value even when the agent is more risk averse.
The paper bridges stochastic control and deep hedging for European call options with transaction costs.
problem Hedging and pricing European call options with proportional transaction costs.
method Complementary perspectives: stochastic control and deep hedging. Two architectures proposed: NTBN-Delta and WW-NTBN.
result WW-NTBN converges faster, matches no-transaction bands more closely, and generalizes well across transaction cost regimes.
This paper investigates the investment behaviour of a large unregulated financial institution (FI) with CARA risk preferences. It shows how the FI optimizes its trading to account for market illiquidity using an extension of the Almgren-Chriss market impact model of multiple risky assets. This expected utility optimiza…
In this paper, we propose an equilibrium pricing model in a dynamic multi-period stochastic framework with uncertain income streams. In an incomplete market, there exist two traded risky assets (e.g. stock/commodity and weather derivative) and a non-traded underlying (e.g. temperature). The risk preferences are of expo…
Model shows incentives in shared order book can lead to free-rider problem.
problem Incentives in shared order books can lead to free-rider problem.
method Developed a Principal-Agent model with CARA utility functions.
result Equilibrium analysis shows incentives can lead to reduced competition.
Study optimizes market making in Chinese stock market with stochastic control and scenario analysis.
problem Limited research on market making in Chinese stock market.
method Optimal market making framework with exponential CARA utility function, accounting for market conditions and risks.
result Impact of volatility and stamp duty on market maker's profit and liquidity.
In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework within which to value derivatives under market impact in a multi-player framework by introducing strategic interactions into the Almgre…
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.
We consider a contracting problem in which a principal hires an agent to manage a risky project. When the agent chooses volatility components of the output process and the principal observes the output continuously, the principal can compute the quadratic variation of the output, but not the individual components. This…
New method for fair resource allocation in AI-aware networks with unknown utility functions.
problem Fair resource allocation in AI-aware communication networks with unknown utility functions.
method Distributed, data-driven bilevel optimization approach to learn surrogate utility functions.
result The proposed algorithm learns from data to autotune surrogate utility functions for unknown utility functions.
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.
New algorithm tackles unknown utility network resource allocation.
problem Maximizing network utility with unknown agent utilities.
method Modeling as a bandit problem, proposing algorithms for resource allocation.
result Proposed algorithms are optimal when all agents have the same utility.
Study robust utility maximization with uncertain continuous semimartingales.
problem Maximizing utility in continuous time under model uncertainty.
method Duality and conjugate problems for logarithmic, exponential, and power utilities.
result Existence of optimal portfolios for various utilities.
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 maximum entropy principle can be used to assign utility values when only partial information is available about the decision maker's preferences. In order to obtain such utility values it is necessary to establish an analogy between probability and utility through the notion of a utility density function. According…
This paper studies stability of the exponential utility maximization when there are small variations on agent's utility function. Two settings are considered. First, in a general semimartingale model where random endowments are present, a sequence of utilities defined on R converges to the exponential utility. Under a …
Study adds investment gains and losses to recursive utility model, proving existence and uniqueness of utility process.
problem Existence and uniqueness of utility process in a recursive utility model with investment gains and losses.
method Generalized recursive utility model with constant elasticity of intertemporal substitution and relative risk aversion degree. Proved existence and uniqueness in a specific, finite-state Markovian setting.
result Utility process exists and is unique when agent derives nonnegative gain-loss utility, and non-existent or non-unique otherwise.
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.
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.
The purpose of this paper relies on the study of long term yield curves modeling. Inspired by the economic litterature, it provides a financial interpretation of the Ramsey rule that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adju…
Study on hedging with delayed strategies for exponential utility maximization.
problem Maximizing exponential utility in semistatic hedging.
method Explicit computations for delayed semistatic hedging.
result Developed methods for hedging with delayed strategies.
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.
We consider market players with tail-risk-seeking behaviour as exemplified by the S-shaped utility introduced by Kahneman and Tversky. We argue that risk measures such as value at risk (VaR) and expected shortfall (ES) are ineffective in constraining such players. We show that, in many standard market models, product d…
Study on robust utility maximization with nonconcave utility functions under projective determinacy.
problem Investor's optimal investment strategy under model ambiguity and nonconcave utility.
method Projective functions of the path and sets of priors, upper-semicontinuous utility.
result Existence of optimal investment strategy under PD.
Investment and consumption strategy optimized under uncertain conditions.
problem Optimal investment and consumption under logarithmic utility and uncertainty model.
method Characterized using quadratic BSDE.
result Optimal solution found.