We study optimal investment problems under the framework of cumulative prospect theory (CPT). A CPT investor makes investment decisions in a single-period financial market with transaction costs. The objective is to seek the optimal investment strategy that maximizes the prospect value of the investor's final wealth. W…
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48 results for “Cumulative Prospect Theory”
In this article, inspired by Shi, et al. we investigate the optimal portfolio selection with one risk-free asset and one risky asset in a multiple period setting under cumulative prospect theory (CPT). Compared with their study, our novelty is that we consider a stochastic benchmark, and portfolio constraints. We test …
We explain the main concepts of Prospect Theory and Cumulative Prospect Theory within the framework of rational dynamic asset pricing theory. We derive option pricing formulas when asset returns are altered with a generalized Prospect Theory value function or a modified Prelec weighting probability function and introdu…
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.
Matching Markets meet Cumulative Prospect Theory: Towards Optimal and Adversarially Robust Learningcs.LG
Matching Markets meet Cumulative Prospect Theory: Towards Optimal and Adversarially Robust Learning
problem Multi-agent multi-armed bandit problem in competitive setup with two-sided matching markets under human-centric decision making model
method Using cumulative prospect theory (CPT) to emulate human preferences
result Improved regret guarantees in adversarial markets with CPT as risk-sensitive measure
The paper addresses human-like decision-making in multi-agent systems using bounded risk-sensitive Markov Games.
problem Modeling human-like decision-making in multi-agent systems with risk-seeking and loss-aversion behaviors.
method Forward policy design and inverse reward learning with iterative reasoning and cumulative prospect theory.
result The proposed algorithms demonstrate both risk-averse and risk-seeking behaviors in multi-agent systems.
We treat a fairly broad class of financial models which includes markets with proportional transaction costs. We consider an investor with cumulative prospect theory preferences and a non-negativity constraint on portfolio wealth. The existence of an optimal strategy is shown in this context in a class of generalized s…
The objective in a traditional reinforcement learning (RL) problem is to find a policy that optimizes the expected value of a performance metric such as the infinite-horizon cumulative discounted or long-run average cost/reward. In practice, optimizing the expected value alone may not be satisfactory, in that it may be…
Study asymptotic properties of generalized shortfall risk measures for heavy-tailed risks.
problem Understanding risk measures for heavy-tailed risks.
method Derive asymptotic expansions for generalized shortfall risk measures.
result Unified theory for risk measures including distortion and utility-based measures.
Within the framework of the cumulative prospective theory of Kahneman and Tversky, this paper considers a continuous-time behavioral portfolio selection problem whose model includes both running and terminal terms in the objective functional. Despite the existence of S-shaped utility functions and probability distortio…
Develops a model for gambling decisions under time inconsistency.
problem Time inconsistency in gambling decisions due to probability weighting in CPT.
method Formulates the problem as a mathematical program, derives optimal precommitted rule.
result Gambler may enter the casino even with limited play, behavior varies based on gains/losses.
We prove the existence of optimal strategies for agents with cumulative prospect theory preferences who trade in a continuous-time illiquid market, transcending known results which pertained only to risk-averse utility maximizers. The arguments exploit an extension of Skorohod's representation theorem for tight sequenc…
We consider an arbitrage-free, discrete time and frictionless market. We prove that an investor maximising the expected utility of her terminal wealth can always find an optimal investment strategy provided that her dissatisfaction of infinite losses is infinite and her utility function is non-decreasing, continuous an…
The study compares parametric and nonparametric models for estimating mean-variance mixtures and finds that nonparametric models perform better.
problem Estimating the distribution of a normal mean-variance mixture under uncertainty.
method Comparison of six parametric mixing laws with a grid nonparametric maximum likelihood estimator, using a paired block bootstrap for score comparison.
result Nonparametric models outperform parametric models in estimating the distribution of a normal mean-variance mixture.
Prospect theory is widely viewed as the best available descriptive model of how people evaluate risk in experimental settings. According to prospect theory, people are risk-averse with respect to gains and risk-seeking with respect to losses, a phenomenon called "loss aversion". Despite of the fact that prospect theory…
Most decision theories, including expected utility theory, rank dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which income is received. Optimal payoffs have their lowest outcomes when the economy …
Optimal exit strategies of CPT gamblers in unfair gambles
problem Optimal exit strategies of gamblers with CPT preferences in games with strictly negative expected payoffs
method Formulating the problem as an optimal stopping problem on asymmetric random walks, applying geometric transformation, randomized strategies, and changing the decision variable
result The unfair problem in the infinite time horizon has finite values for a wide range of CPT parameter specifications
Continuous-Time Portfolio Optimisation for a Behavioural Investor with Bounded Utility on Gainsq-fin.PM
This paper examines an optimal investment problem in a continuous-time (essentially) complete financial market with a finite horizon. We deal with an investor who behaves consistently with principles of Cumulative Prospect Theory, and whose utility function on gains is bounded above. The well-posedness of the optimisat…
Develops uniform convergence guarantees for a broad class of risk functionals in supervised learning.
problem Bounding generalization gaps for various risk functionals beyond the expectation.
method Establishes uniform convergence for Hölder risk functionals, providing guarantees for empirical risk minimization.
result First uniform convergence results for estimating the CDF of loss distributions, applicable to various risk functionals.
The most commonly accepted model for investors' preferences is expected utility theory. More recently, other theories have emerged and pose new challenges to mathematics. The present paper treats preferences of cumulative prospect theory (CPT), where an "S-shaped" utility function is considered (i.e. convex up to a cer…
The paper tackles robust control for insurance contracts under uncertain transition rates.
problem Maximizing utility in insurance contracts with uncertain transition rates.
method Novel robust utility maximization problem under bounded cumulative transition rate uncertainty, using worst-case scenario analysis.
result Existence and uniqueness of worst-case and best-case reserves for insurance contracts.
Artificial intelligence has impacted many aspects of human life. This paper studies the impact of artificial intelligence on economic theory. In particular we study the impact of artificial intelligence on the theory of bounded rationality, efficient market hypothesis and prospect theory.
Investigates optimal strategies for behavioral control problems with finite variation controls.
problem Behavioral singular stochastic control problems with finite variation controls.
method Abstract framework, applied to storage management and portfolio investment problems, using CPT preferences and Skorokhod representation theorem.
result Existence of optimal strategies for various goal functionals, including CPT preferences.
Many investment models in discrete or continuous-time settings boil down to maximizing an objective of the quantile function of the decision variable. This quantile optimization problem is known as the quantile formulation of the original investment problem. Under certain monotonicity assumptions, several schemes to so…
New methods evaluate stock market anomalies for prospect investors.
problem Determining if new securities or investment changes improve prospect investors' opportunities.
method Developed and implemented a new testing procedure for prospect spanning using subsampling and Linear Programming.
result Many well-known anomalies expand prospect investors' opportunity sets, indicating real economic value.
Proposes a new framework for optimizing utility with state-dependent benchmarks.
problem Various interpretations of benchmarks in utility functions.
method General framework of state-dependent utility optimization with stochastic benchmarks.
result Provides optimal solutions and addresses issues of well-definedness and feasibility.
This paper formulates and studies a general continuous-time behavioral portfolio selection model under Kahneman and Tversky's (cumulative) prospect theory, featuring S-shaped utility (value) functions and probability distortions. Unlike the conventional expected utility maximization model, such a behavioral model could…
We show that, in a resource allocation problem, the ex ante aggregate utility of players with cumulative-prospect-theoretic preferences can be increased over deterministic allocations by implementing lotteries. We formulate an optimization problem, called the system problem, to find the optimal lottery allocation. The …
Estimates boundaries for acceptable bilateral gamma risk in financial markets.
problem Determining the compensation needed for risky future cash flows to be considered acceptable.
method Statistical inference from market prices and derivatives, using prospect theory.
result Upper and lower boundaries for bilateral gamma risk are estimated and tested against market data.
A speculative agent with Prospect Theory preference chooses the optimal time to purchase and then to sell an indivisible risky asset to maximize the expected utility of the round-trip profit net of transaction costs. The optimization problem is formulated as a sequential optimal stopping problem and we provide a comple…
Prospective learning improves AI performance in changing conditions.
problem Machine learning algorithms struggle with changing data distributions and evolving goals.
method Developed a new mathematical framework called Prospective Learning.
result Preliminary results show improved algorithm performance and applicability to sequential decision-making.
Develops a new learning framework for dynamic data.
problem Poor performance of existing strategies in dynamic data and goals.
method Prospective Learning framework and Prospective ERM algorithm.
result Prospective ERM converges to Bayes risk under certain assumptions.
Study derives new equation for reserves in non-monotone information scenarios.
problem Modeling reserves in situations where information is not always increasing.
method Infinitesimal approach to derive generalized stochastic Thiele equation.
result New equation allows for information discarding and solves open problems.
On the Past, Present, and Future of the Diebold-Yilmaz Approach to Dynamic Network Connectednessecon.EM
Retrospective and prospective analysis of Diebold-Yilmaz connectedness research.
problem Assessing the Diebold-Yilmaz approach to dynamic network connectedness.
method Retrospective and prospective analysis of Diebold-Yilmaz (2014) and personal recollections.
result Personal insights and retrospective analysis of Diebold-Yilmaz connectedness research.
Review and Prospect of Algebraic Research in Equivalent Framework between Statistical Mechanics and Machine Learning Theorycond-mat.stat-mech
Paper reviews algebraic research in machine learning theory.
problem Understanding phase transitions in machine learning models.
method Algebraic approaches in statistical mechanics.
result Algebraic methods are essential for analyzing machine learning models with singularities.
In this paper we build a method to optimize Multi-Year Prospective Budgets. First we present a systemic model of Local Community Finances. Then, from two acceptable Multi-Year Prospective Budgets the method implements a Genetic Algorithm to generate a collection of admissible Multi-Year Prospective Budgets among which …
This work explores a social learning problem with agents having nonidentical noise variances and mismatched beliefs. We consider an -agent binary hypothesis test in which each agent sequentially makes a decision based not only on a private observation, but also on preceding agents' decisions. In addition, the agents…
PsychFM predicts individual gambling choices using psychological and machine learning models.
problem Predicting individual gambling choices with high precision.
method PsychFM combines machine learning and psychological theories.
result PsychFM outperforms existing models like random forest and factorization machines.
The study examines higher-order modern portfolio theory with complex critical points and feasible portfolio variety.
problem Understanding the complex critical points and feasible portfolio variety in higher-order modern portfolio theory.
method Established genericity conditions for utility functions with higher-order cumulants, analyzed discriminant loci, and determined the dimension and degree of the feasible portfolio variety.
result The utility function has a constant number of complex critical points under genericity conditions, and the feasible portfolio variety has a determined dimension and degree.
Data science enhances knot theory by analyzing invariant relations.
problem Understanding the complex relations between knot invariants.
method Topological data analysis applied to knot theory.
result New insights into long-standing conjectures about knots.
We consider the -ary classification problem via crowdsourcing, where crowd workers respond to simple binary questions and the answers are aggregated via decision fusion. The workers have a reject option to skip answering a question when they do not have the expertise, or when the confidence of answering that questio…
A microeconomic approach is proposed to derive the fluctuations of risky asset price, where the market participants are modeled as prospect trading agents. As asset price is generated by the temporary equilibrium between demand and supply, the agents' trading behaviors can affect the price process in turn, which is cal…
Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costsq-fin.MF
In discrete time markets with proportional transaction costs, Schachermayer (2004) shows that robust no-arbitrage is equivalent to the existence of a strictly consistent price system. In this paper, we introduce the concept of prospective strict no-arbitrage that is a variant of the strict no-arbitrage property from Ka…
Managing large-scale transportation infrastructure projects is difficult due to frequent misinformation about the costs which results in large cost overruns that often threaten the overall project viability. This paper investigates the explanations for cost overruns that are given in the literature. Overall, four categ…
We propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree. Instead of minimizing an objective f…
This paper presents a unified approach based on Wasserstein distance to derive concentration bounds for empirical estimates for two broad classes of risk measures defined in the paper. The classes of risk measures introduced include as special cases well known risk measures from the finance literature such as condition…
Study shows short exposure and systematic risk exposure affect disposition effect asymmetries.
problem Understanding disposition effect in short vs long exposure positions and systematic risk.
method Generalized Odean measures, introduced Value metric, implemented dispositionEffect R package.
result Short positions exhibit weaker disposition effect than long positions under narrow framing, reversing in integrated framing.
Reinforcement Learning (RL) has demonstrated a great potential for automatically solving decision-making problems in complex uncertain environments. RL proposes a computational approach that allows learning through interaction in an environment with stochastic behavior, where agents take actions to maximize some cumula…