Expected Utility Maximization Research Articles

Non-diversified portfolios with subjective expected utility

Diversification is the typical investment strategy of risk-averse agents. However, non-diversified positions that allocate all resources to a single asset, state of the world or revenue stream are common too. We show that whenever finitely many non-diversified demands under uncertainty are compatible with risk-averse subjective expected utility maximization under strictly positive beliefs, they are also rationalizable under the same beliefs by many qualitatively distinct risk-averse as well as risk-neutral and risk-seeking preferences.

Choices under uncertainty and the investment horizon

AbstractMean–Variance (M–V) is the most popular investment rule employed by both practitioners and researches. For a short-planned investment horizon, this rule generally conforms with expected utility paradigm. However, for a relatively long horizon, generally more than one year, the distributions of returns become positively skewed, hence the M–V rule loses ground. As the horizon increases, by the M–V rule one needs (mistakenly) to increase the weight of bonds in the stock–bond portfolio, e.g., almost 100% in bonds for a 30-year horizon. Expected utility maximization recommending almost 100% in stocks for long horizons. This, gap is of crucial importance, because life expectancy is increasing, implying longer investment horizons. For long horizons the mean–coefficient-of-variance rule conforms with expected utility, as the distributions are close to log-normal. For intermediate horizons one should employ stochastic dominance or direct expected utility maximization.

Optimal Market Completion through Financial Derivatives with Applications to Volatility Risk

This paper investigates the optimal choices of financial derivatives to complete a financial market in the framework of stochastic volatility (SV) models. We first introduce an efficient and accurate simulation-based method applicable to generalized diffusion models to approximate the optimal derivatives-based portfolio strategy. We build upon a double optimization approach, i.e., expected utility maximization and risk exposure minimization, already proposed in the literature, demonstrating that strangle options are the best choices for market completion within equity options. They lead to lower investors’ risk exposure for a wide range of strikes compared to the lesser flexibility of calls, puts, and strangles. Furthermore, we explore the benefit of using volatility index derivatives and conclude that they could be more convenient substitutes when short-term maturity equity options are not available.

Resource-rational psychopathology.

Psychopathology is vast and diverse. Across distinct disease states, individuals exhibit symptoms that appear counter to the standard view of rationality (expected utility maximization). We argue that some aspects of psychopathology can be described as resource-rational, reflecting a rational trade-off between reward and cognitive resources. We review work on two theories of this kind: rational inattention, where a capacity limit applies to perceptual channels, and policy compression, where the capacity limit applies to action channels. We show how these theories can parsimoniously explain many forms of psychopathology, including affective, primary psychotic, and neurodevelopmental disorders, as well as many effects of psychoactive medications on these disorders. While there are important disorder-specific differences and the theories are by no means universal, we argue that resource rationality offers a useful new perspective on psychopathology. By emphasizing the role of cognitive resource constraints, this approach offers a more inclusive picture of rationality. Some aspects of psychopathology may reflect rational trade-offs rather than the breakdown of rationality. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Does correlation matter in probability matching? A laboratory investigation

Probability Matching, a classical violation of expected utility maximization, refers to people's tendency to randomize, or even match their choice frequency to the outcome probability, when choosing over binary lotteries that differ only in their probabilities. Why? I present an experiment designed to distinguish between several broad classes of explanations: (1) models of Correlation-Invariant Stochastic Choice — randomizing due to factors orthogonal to the correlation between lotteries, such as non-standard preferences or errors, and (2) models of Correlation-Sensitive Stochastic Choice — deliberately randomizing due to misperceived hedging opportunities, especially when lotteries are negatively correlated. My experimental design differentiates between their testable predictions by varying the correlation between lottery outcomes. The findings indicate that the first class, despite being home to most existing theories, has limited explanatory power. Using additional treatment, I rule out Similarity Heuristics as a competing explanation with the second class. The results indicate that a vast majority of individuals deliberately randomize due to misperceived hedging opportunities.

Sophisticated reasoning, learning, and equilibrium in repeated games with imperfect feedback

AbstractWe analyze the infinite repetition with imperfect feedback of a simultaneous or sequential game, assuming that players are strategically sophisticated—but impatient—expected-utility maximizers. Sophisticated strategic reasoning in the repeated game is combined with belief updating to provide a foundation for a refinement of self-confirming equilibrium. In particular, we model strategic sophistication as rationality and common strong belief in rationality. Then, we combine belief updating and sophisticated reasoning to provide sufficient conditions for a kind of learning—that is, the ability, in the limit, to exactly forecast the sequence of future observations—thus showing that impatient agents end up playing a sequence of self-confirming equilibria in strongly rationalizable conjectures of the one-period game.

Conformal prediction for stochastic decision-making of PV power in electricity markets

This paper studies the use of conformal prediction (CP), an emerging probabilistic forecasting method, for day-ahead photovoltaic power predictions to enhance participation in electricity markets. First, machine learning models are used to construct point predictions. Thereafter, several variants of CP are implemented to quantify the uncertainty of those predictions by creating CP intervals and cumulative distribution functions. Optimal quantity bids for the electricity market are estimated using several bidding strategies under uncertainty, namely: trust-the-forecast, worst-case, Newsvendor and expected utility maximization (EUM). Results show that CP in combination with k-nearest neighbors and/or Mondrian binning outperforms its corresponding linear quantile regressors. Using CP in combination with certain bidding strategies can yield high profit with minimal energy imbalance. In concrete, using conformal predictive systems with k-nearest neighbors and Mondrian binning after random forest regression yields the best profit and imbalance regardless of the decision-making strategy. Combining this uncertainty quantification method with the EUM strategy with conditional value at risk (CVaR) can yield up to 93% of the potential profit with minimal energy imbalance.

Better Foundations for Subjective Probability

ABSTRACT How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences. However, standard representation theorems make strong rationality assumptions, in particular expected utility maximization. How do we ascribe subjective probability to agents which do not satisfy these strong rationality assumptions? I present a representation theorem with weak rationality assumptions which can be used to define or measure subjective probability for partly irrational agents.

Budget-Constrained Linear Utility Maximization and the Hurwicz (1951) Criterion

We show that for a trader displaying state-dependent risk-neutrality, budget constrained maximization based on the Hurwicz criterion for “non-probabilistic” uncertainty with the degree of pessimism being less than half, reduces to expected utility maximization under “the equal ignorance principle”, with all wealth being invested in positive return being available in just one state of nature and nothing at all in other states of nature. Such a portfolio is an extreme point of the set of budget-constrained expected utility maximizing portfolios, with equiprobable states of nature. With more than two uncertain states of nature, the above result extends to the case where the degree of pessimism is equal to half. We also show that if for a degree of pessimism, greater than or equal to half, an optimal solution to budget constrained maximization based on the Hurwicz criterion is not of this type, then it must be a “budget-constrained max-min utility maximizing” portfolio.

Credence and Belief: Distance- and Utility-Based Approaches

Abstract This paper investigates the question of how subjective probability should relate to binary belief. We propose new distance minimization methods, and develop epistemic decision-theoretic accounts. Both approaches can be shown to get “close” to the truth: the first one by getting “close” to a given probability, and the second by getting expectedly “close” to the truth. More specifically, we study distance minimization with a refined notion of Bregman divergence and expected utility maximization with strict proper scores. Our main results reveal that the two ways to get “close” to the truth can coincide.

A Study on the Impact of Demographics Variable on Mental Accounting Bias of Individual Investors in Financial Decision

It has been asserted that investors' preferences for equities are influenced by their desires, cognitive flaws, and emotions. A succinct introduction to behavioural finance is given in this article. Research that rejects the conventional premises of expected utility maximisation with logical investors in efficient markets is referred to as behavioural finance. The study of psychology, according to financial economists, can explain stock market anomalies, market booms, and crashes as well as shed significant light on how unpredictable and erratic human behaviour can be. This has the potential to challenge the conventional wisdom that financial markets operate efficiently. Mental accounting bias is depicted in investor behaviour where Investors split their funds into many mental account tiers of a portfolio pyramid in order to achieve objectives like securing their retirement funds, paying for their kid's college, or being able to travel the world. In accordance with the organization's power, the law, and its obligation commitments, the paper outlines ideas to improve the efficacy of financial decisions and identifies the psychological effects' limitations. In Practical, proposals about the adoption, execution, and evaluation of financial decisions were made considering scarce funds and rising need.

Optimal reinsurance-investment problem with default risk for an insurer under the constant elasticity of variance model

Abstract Accepted by: Giorgio Consigli In this paper we study the optimal reinsurance-investment problem for an insurer with constant absolute risk aversion (CARA) utility. Because the insurer needs to avoid large claims and make profits in the actual operation process, he/she is allowed to buy proportional reinsurance and invest in a risk-free bond, a stock and a default bond. Moreover, the price process of the stock follows the constant elasticity of variance (CEV) model and the correlation between the risk process and the stock’s price is considered. For the objective of expected utility maximization, we establish the Hamilton–Jacobi–Bellman equation and derive the optimal reinsurance-investment strategy explicitly for the pre-default case and the post-default case via the dynamic programming. Finally, numerical examples and sensitivity analyses are provided to illustrate the effects of model parameters on the optimal strategy. We find that (i) the default risk has no impact on the optimal strategy of the stock and the parameters of the stock’s price have no impact on the optimal money amount invested in the defaultable bond. (ii) The optimal reinsurance strategy depends on the volatility of the stock’s price under the CEV model. (iii) The correlation between risk model and the stock’s price does have effects on the insurer’s optimal reinsurance-investment strategy. These findings may provide guidance to the management of insurers in practice.

The impact of ambiguity on dynamic portfolio selection in the epsilon-contaminated binomial market model

We consider dynamic portfolio selection under ambiguity in the classical multi-period binomial market model. Ambiguity is incorporated in the real-world probability measure through an epsilon-contamination, that gives rise to a completely monotone capacity conveying a pessimistic investor’s ambiguous beliefs. The dynamic portfolio selection problem is formulated as a Choquet expected utility maximization problem on the final wealth. Then, the optimal final wealth is proved to be a function of the final stock price: this allows a dimension reduction of the problem, switching from an exponential to a linear size with respect to the number of periods. Finally, an explicit characterization of the optimal final wealth is given in the case of a constant relative risk aversion utility function and the interaction between the ambiguity and the relative risk aversion parameters is investigated.

The development gap in economic rationality of future elites

We test the touchstones of economic rationality—utility maximization, stochastic dominance, and expected-utility maximization—of elite students in the U.S. and in Africa. The choices of most students in both samples are generally rationalizable, but the U.S. students' scores are substantially higher. Nevertheless, the development gap in economic rationality in incentivized risk choices between these future elites is much smaller than the difference in performance on a non-incentivized canonical cognitive ability test, often used as a proxy for economic decision-making ability in studies of economic development and growth. We argue for the importance of including consistency with economic rationality in studies of decision-making ability.

Robust optimal asset-liability management with mispricing and stochastic factor market dynamics

This paper investigates a robust optimal asset-liability management problem under an expected utility maximization criterion. More specifically, the manager is concerned about the potential model uncertainty and aims to seek the robust optimal investment strategies. We incorporate an uncontrollable random liability described by a generalized drifted Brownian motion. Also, the manager has access to an incomplete financial market consisting of a risk-free asset, a market index with potentially path-dependent, time-varying risk premium and volatility, and a pair of mispriced stocks. The market dynamics are assumed to rely on an affine-form, square-root factor process and the price error is modeled by a co-integrated system. We adopt a backward stochastic differential equation approach hinging on the martingale optimality principle to solve this non-Markovian robust control problem. Closed-form expressions for the robust optimal investment strategies, the probability perturbation process under the well-defined worst-case scenario and the corresponding value function are derived. The admissibility of the robust optimal controls is verified under some technical conditions. Finally, we perform some numerical examples to illustrate the effects of model parameters on the robust investment strategies and draw some economic interpretations from these results.

Managing Weather Risk with a Neural Network-Based Index Insurance

Weather risk affects the economy, agricultural production in particular. Index insurance is a promising tool to hedge against weather risk, but current piecewise-linear index insurance contracts face large basis risk and low demand. We propose embedding a neural network-based optimization scheme into an expected utility maximization problem to design the index insurance contract. Neural networks capture a highly nonlinear relationship between the high-dimensional weather variables and production losses. We endogenously solve for the optimal insurance premium and demand. This approach reduces basis risk, lowers insurance premiums, and improves farmers’ utility. This paper was accepted by Agostino Capponi, finance. Funding: This work was supported by the Research Grants Council, University Grants Committee [Grants GRF 16502020, GRF 16504522, and T31-603/21-N], Singapore Ministry of Education Academic Research Fund Tier 1 [Grants RG143/19 and RG55/20], the Natural Sciences and Engineering Research Council of Canada [Grants RGPIN-2021-04144 and DGECR-2021-00330], the Research Database Matching Fund, and the School of Business and Management, Hong Kong University of Science and Technology. Supplemental Material: The data files and online appendices are available at https://doi.org/10.1287/mnsc.2023.4902 .

Optimal Consumption and Investment Problem under 4/2-CIR Stochastic Hybrid Model

In this paper, we investigate the optimal consumption and investment problem under the expected utility maximization criterion. It is supposed that the financial market consists of a risky asset and a risk-free asset, and the risky asset prices follow the 4/2 Cox–Ingersoll–Ross (CIR) stochastic hybrid model. The investment objective is to obtain an optimal consumption–investment strategy by maximizing the objective function. The closed-form expression of the optimal consumption–investment strategy is obtained by using optimal control theory and the corresponding Hamilton–Jacobi–Bellman (HJB) equation under the power utility function. In addition, we present a numerical example to illustrate the influence of model parameters on the optimal consumption–investment strategy.

Non-concave Expected Utility Optimization with Uncertain Time Horizon

We consider an expected utility maximization problem where the utility function is not necessarily concave and the time horizon is uncertain. We establish a necessary and sufficient condition for the optimality for general non-concave utility function in a complete financial market. We show that the general concavification approach of the utility function to deal with non-concavity, while being still applicable when the time horizon is a stopping time with respect to the financial market filtration, leads to sub-optimality when the time horizon is independent of the financial risk, and hence can not be directly applied. For the latter case, we suggest a recursive procedure which is based on the dynamic programming principle. We illustrate our findings by carrying out a multi-period numerical analysis for optimal investment problem under a convex option compensation scheme with random time horizon. We observe that the distribution of the non-concave portfolio in both certain and uncertain random time horizon is right-skewed with a long right tail, indicating that the investor expects frequent small losses and a few large gains from the investment. While the (certain) average time horizon portfolio at a premature stopping date is unimodal, the random time horizon portfolio is multimodal distributed which provides the investor a certain flexibility of switching between the local maximizers, depending on the market performance. The multimodal structure with multiple peaks of different heights can be explained by the concavification procedure, whereas the distribution of the time horizon has significant impact on the amplitude between the modes.

Bowley Insurance with Expected Utility Maximization of the Policyholders

This article studies the Bowley solution for a sequential game within the expected utility framework. We assume that the policyholders are expected utility maximizers and there exists a representative policyholder who faces a fixed loss with given probability and no loss otherwise. This policyholder selects the optimal indemnity function in response to the pricing kernel set by the insurer. Knowing the policyholder’s choice of indemnity function, the insurer adjusts the pricing kernel to maximize its expected net profit. This pricing kernel is of our central interest in this article, and in our setting the pricing kernel can be evaluated via the safety loading factor in an expected value premium principle. For a wide class of utility functions, we show that the optimal safety loading factor increases with respect to both the policyholder’s risk aversion level and the probability of zero loss. We also show that the insurance contract corresponding to the Bowley solution is Pareto dominated in the sense that both parties’ interests can be further improved, which shows the inefficiency of the Bowley solution. Some numerical examples are presented to illustrate the main results, and it is shown that both the policyholder and insurer can strictly benefit from the Bowley solution.

Intergenerational risk sharing in a defined contribution pension system: analysis with Bayesian optimization

AbstractWe study a fully funded, collective defined contribution (DC) pension system with multiple overlapping generations. We investigate whether the welfare of participants can be improved by intergenerational risk sharing (IRS) implemented with a realistic investment strategy (e.g., no borrowing) and without an outside entity (e.g., shareholders) that helps finance the pension fund. To implement IRS, the pension system uses an automatic adjustment rule for the indexation of individual accounts, which adapts to the notional funding ratio of the pension system. The pension system has two parameters that determine the investment strategy and the strength of the adjustment rule, which are optimized by expected utility maximization using Bayesian optimization. The volatility of the retirement benefits and that of the funding ratio are analyzed, and it is shown that the trade-off between them can be controlled by the optimal adjustment parameter to attain IRS. Compared with the optimal individual DC benchmark using the life cycle strategy, the studied pension system with IRS is shown to improve the welfare of risk-averse participants, when the financial market is volatile.