Dual moments replace primal moments for measuring risk aversion.
problem Traditional risk aversion measures using mean and variance are insufficient in non-EU models.
method Introduced dual moments as a new measure for absolute risk aversion.
result Dual moments provide an equivalent index of absolute risk aversion in non-EU models.
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.
The comparative statics of the optimal portfolios across individuals is carried out for a continuous-time complete market model, where the risky assets price process follows a joint geometric Brownian motion with time-dependent and deterministic coefficients. It turns out that the indirect utility functions inherit the…
Under expected utility the local index of absolute risk aversion has played a central role in many applications. Besides, its link with the "global" concepts of the risk and probability premia has reinforced its attractiveness. This paper shows that, with an appropriate approach, similar developments can be achieved in…
Derives a new formula for measuring risk aversion in markets.
problem Measuring the degree of risk aversion in markets accurately.
method Closed-form expression based on three variables: Treasury yields, returns, and market capitalization.
result Investors exhibit Decreasing Absolute Risk Aversion (DARA) but the degree of Relative Risk Aversion (RRA) varies.
For an investor with constant absolute risk aversion and a long horizon, who trades in a market with constant investment opportunities and small proportional transaction costs, we obtain explicitly the optimal investment policy, its implied welfare, liquidity premium, and trading volume. We identify these quantities as…
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.
Optimal liquidation strategy for a risk-averse investor in a one-sided limit order book driven by a Levy process.
problem Balancing market risk and execution cost for a large share liquidation.
method Modeling the price process as a Levy process and solving a singular two-dimensional optimisation problem.
result Explicit expression for the optimal intervention boundary.
Study optimal dynamic basis trading strategies with stochastic basis model.
problem Optimal dynamic trading of futures and underlying asset under stochastic basis.
method Model basis evolution as stopped scaled Brownian bridge, solve utility maximization problem with HARA risk preferences.
result Derive exact conditions for optimal trading strategies and solve explicitly.
Assuming that agents' preferences satisfy first-order stochastic dominance, we show how the Expected Utility paradigm can rationalize all optimal investment choices: the optimal investment strategy in any behavioral law-invariant (state-independent) setting corresponds to the optimum for an expected utility maximizer w…
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.
We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semi-martingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference price converges to a well defined limit, we prove that optimally taken position…
On a capital market the social group is formed from traders. Individual behaviour of agents is influenced by the need to associate with other agents and to obtain the approval of other agents in the group. Making decisions an individual equates own needs with those of the other agents. Any two agents from the group may…
This paper presents non-parametric estimates of spectral risk measures applied to long and short positions in 5 prominent equity futures contracts. It also compares these to estimates of two popular alternative measures, the Value-at-Risk (VaR) and Expected Shortfall (ES). The spectral risk measures are conditioned on …
We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, Itô-process models of financial markets with random ergodic coefficients. Including {\em value-at-risk} (VaR), {\em tail-value-at-risk} (TVaR), and {\em limited expected loss} (LEL), these cons…
Optimizes pension fund strategies considering age-dependent risk preferences.
problem Maximizing utility of future consumption and wealth in DC pension plans.
method Solves optimal consumption and investment policies using Black-Scholes framework and HARA utility functions.
result Only extended model with time-varying preference parameters provides adequate fit for real-life data.
MVPI framework optimizes risk in reinforcement learning, improving performance in robot simulations.
problem Optimizing risk in reinforcement learning control problems.
method Mean-Variance Policy Iteration (MVPI) framework for risk-averse control in MDPs.
result Risk-averse TD3 outperforms previous methods in robot simulation tasks.
A new measure quantifies how risk-averse different risk measures are.
problem Measuring the degree of risk aversion among different risk measures.
method Two axioms: normalization and linearity. Two formulas for the functional.
result Quantifies the degree of risk aversion among spectral risk measures.
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.
An investor with constant absolute risk aversion trades a risky asset with general Itô-dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading-order optimal trading policy and the associated welfare, expressed in terms of the local dynamics of the frictionless op…
Paper develops a new framework for analyzing certainty equivalents and dynamic risk premia using Malliavin calculus and Wiener chaos analysis.
problem Limitations of Arrow-Pratt approximation for arbitrary sequences of vanishing risks.
method Develops a new framework based on Malliavin calculus and Wiener chaos analysis, combining Itô calculus, the Clark--Ocone representation, and the Wiener chaos decomposition.
result Establishes a unified framework linking expected utility theory, stochastic analysis, and Wiener chaos expansions, revealing higher-order certainty equivalents and dynamic risk premia.
Investigates how diversification preferences relate to risk attitudes.
problem Connecting diversification preferences to risk attitudes.
method Analyzes diversification preferences for various pairs of risks under different conditions.
result Diversification preferences for certain pairs of risks imply specific levels of risk aversion.
Different models of capital exchange among economic agents have been proposed recently trying to explain the emergence of Pareto's wealth power law distribution. One important factor to be considered is the existence of risk aversion. In this paper we study a model where agents posses different levels of risk aversion,…
Robo-advisors estimate clients' risk aversion using interactive questionnaires.
problem Estimating risk aversion of non-expert clients using adaptive questionnaires.
method Model risk aversion with cost functions and spectral risk measures. Use inverse reinforcement learning to design questions maximizing distinguishing power.
result Designing questions by maximizing distinguishing power achieves satisfactory accuracy in learning risk aversion with fewer than 50 questions.
Optimal trading patterns adjust based on market efficiency and slippage costs.
problem Balancing active alphas and trading costs in active portfolios.
method Maximization of utility including projected alpha-based profits, slippage costs, and risk aversion.
result Optimal trading involves a no-trade zone width that scales as Δ∼c1/2, differing from stochastic settings. Risk aversion is a key element of utility maximizing hedge strategies; however, it has typically been assigned an arbitrary value in the literature. This paper instead applies a GARCH-in-Mean (GARCH-M) model to estimate a time-varying measure of risk aversion that is based on the observed risk preferences of energy hed…
Modeling informed trading with risk-averse market makers.
problem Understanding informed trading and its impact on market liquidity and risk premia.
method Connections between optimal transport theory and Kyle's model, including new characterizations of profits and duality.
result Liquidity is lower, assets exhibit short-term reversals, and risk premia depend on market maker inventories, which are mean reverting.
Paper improves fractional trading for risk-averse investors by considering current drawdowns.
problem Optimizing trading strategies for risk-averse investors.
method Reconsidered fractional trading ansatz with current drawdown risk measure.
result Optimal fraction solutions better reflect risk-averse investor needs.
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 an investor with constant absolute risk aversion who trades a risky asset with general Ito dynamics, in the presence of small proportional transaction costs. Kallsen and Muhle-Karbe (2012) formally derived the leading-order optimal trading policy and the associated welfare impact of transaction costs. In th…
A new algorithm avoids worst-case outcomes in risky contexts.
problem Risk-averse behavior in contextual bandits is challenging.
method Developed a first risk-averse contextual bandit algorithm with online regret guarantees.
result First algorithm with an online regret guarantee for risk-averse contextual bandits.
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…
Study risk-averse insider's behavior in dynamic signal asset pricing.
problem Analyzing risk-averse insider's dynamic signal in asset pricing.
method Employing a weak conditioning methodology to construct a Schrödinger bridge, deriving necessary conditions for equilibrium.
result Derive explicit closed-form solutions for important cases.
The standard asset pricing models (the CCAPM and the Epstein-Zin non-expected utility model) counterintuitively predict that equilibrium asset prices can rise if the representative agent's risk aversion increases. If the income effect, which implies enhanced saving as a result of an increase in risk aversion, dominates…
Paper develops NPG for risk-averse RL with ECRMs, proving global convergence.
problem Ensuring reliable performance in stochastic RL problems with risk-averse policies.
method Developed natural policy gradient updates for ECRMs-based RL problems, proving global optimality and iteration complexity.
result Global convergence of risk-averse NPG algorithm with ECRMs.
Paper estimates spectral risk measures for insurance data with truncated and censored data.
problem Estimating spectral risk measures for insurance data with left truncation and right censoring.
method Proposes a non-parametric estimator using product limit estimator and establishes asymptotic normality.
result Proposed estimator outperforms existing methods for small k and small sample sizes.
New insights into risk aversion for complex decision models.
problem Understanding risk aversion in non-monotone decision models.
method Characterization of probabilistic risk aversion for generalized rank-dependent functions.
result Probabilistic risk aversion is determined by the distortion function, which is convex or scaled quantile-spread mixtures.
The paper examines how loss aversion impacts multi-armed bandit decisions over long periods.
problem The impact of loss aversion on multi-armed bandit decisions over long periods.
method A new central limit theorem for measures with history-dependent variances, derived under risk aversion in gains and risk loving in losses.
result Consequences of loss aversion for asymptotic properties are derived in analytical results.
Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their risk-aversion functions. To date there has been very little guidance on the choice of risk-aversion functions underlying spectral risk measures. This paper addresses this issue by examining two popular …
One index satisfies the duality axiom if one agent, who is uniformly more risk-averse than another, accepts a gamble, the latter accepts any less risky gamble under the index. Aumann and Serrano (2008) show that only one index defined for so-called gambles satisfies the duality and positive homogeneity axioms. We call …
Proposes a new risk measurement method for risk-averse stochastic optimization.
problem Risk-averse stochastic optimization problems.
method Develops a risk measure based on argmin and minimum concepts.
result Guarantees the existence of solutions for the proposed problem.
Risk-averse approach for online convex bandit problems.
problem Online convex optimization with bandit feedback for risk-averse decision makers.
method Two algorithms: descent-type and ellipsoid method-based.
result Achieves optimal regret bounds for risk-aversion.
High subjective discount and risk aversion contradict financial data.
problem Inconsistent asset pricing with financial stylised facts.
method Analyzing capital market equilibrium restrictions.
result Subjective discount and risk aversion cannot be high simultaneously.
Deep Hedging learns optimal strategies for various risk levels.
problem Finding optimal hedging policies for diverse risk aversions.
method Continuous Reinforcement Learning with actor-critic algorithm.
result Demonstrated effectiveness in a stochastic volatility model.
The paper proves conditions for Jensen's inequality with Choquet integral and applies it to risk aversion.
problem Conditions for Jensen's inequality with generalized Choquet integral.
method Analyzes necessary and sufficient conditions for Jensen's inequality for the generalized Choquet integral.
result Generalized Arrow-Pratt theorem for risk aversion using generalized Choquet integral.
New methods reduce bias in estimating optimality gaps for risk-averse stochastic programs.
problem Optimality gap estimation bias in risk-averse stochastic programs.
method Two independent samples, each estimating a different component of the optimality gap.
result Our method reduces bias in estimating optimality gaps for risk-averse problems.
Stochastic domains often involve risk-averse decision makers. While recent work has focused on how to model risk in Markov decision processes using risk measures, it has not addressed the problem of solving large risk-averse formulations. In this paper, we propose and analyze a new method for solving large risk-averse …
Enhances financial risk quantification in classical models.
problem Risk quantification in classical finance models.
method Nested risk measures, limiting behavior analysis.
result Uniqueness of risk-averse limit in classical models.