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on Utility Models and Prospect Theory |
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Issue of 2023‒08‒28
twelve papers chosen by |
| By: | Laurence Carassus; Massinissa Ferhoune |
| Abstract: | We study a robust utility maximization problem in a general discrete-time frictionless market under quasi-sure no-arbitrage. The investor is assumed to have a random and concave utility function defined on the whole real-line. She also faces model ambiguity on her beliefs about the market, which is modeled through a set of priors. We prove the existence of an optimal investment strategy using only primal methods. For that we assume classical assumptions on the market and on the random utility function as asymptotic elasticity constraints. Most of our other assumptions are stated on a prior-by-prior basis and correspond to generally accepted assumptions in the literature on markets without ambiguity. We also introduce utility functions of type (A), which include utility functions with benchmark and for which our assumptions are easily checked. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.11919&r=upt |
| By: | Ananya Parashar; Ludovic Tangpi |
| Abstract: | In this paper, we study the portfolio optimization problem formulated by Lacker and Soret. They formulate a finite time horizon model that allows agents to be competitive, measuring their utility not only by their absolute wealth but also relative performance compared to the average of other agents. While the finite population or $n$-player game is tractable in some cases, the authors present the Mean Field Game framework to solve this problem. Here, we seek to use this framework to clearly detail the optimal investment and consumption strategies in the CRRA utility case as was briefly outlined in Lacker and Soret, but also derive a solution in the CARA utility case. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.10540&r=upt |
| By: | Steve Phelps; Rebecca Ranson |
| Abstract: | AI Alignment is often presented as an interaction between a single designer and an artificial agent in which the designer attempts to ensure the agent's behavior is consistent with its purpose, and risks arise solely because of conflicts caused by inadvertent misalignment between the utility function intended by the designer and the resulting internal utility function of the agent. With the advent of agents instantiated with large-language models (LLMs), which are typically pre-trained, we argue this does not capture the essential aspects of AI safety because in the real world there is not a one-to-one correspondence between designer and agent, and the many agents, both artificial and human, have heterogeneous values. Therefore, there is an economic aspect to AI safety and the principal-agent problem is likely to arise. In a principal-agent problem conflict arises because of information asymmetry together with inherent misalignment between the utility of the agent and its principal, and this inherent misalignment cannot be overcome by coercing the agent into adopting a desired utility function through training. We argue the assumptions underlying principal-agent problems are crucial to capturing the essence of safety problems involving pre-trained AI models in real-world situations. Taking an empirical approach to AI safety, we investigate how GPT models respond in principal-agent conflicts. We find that agents based on both GPT-3.5 and GPT-4 override their principal's objectives in a simple online shopping task, showing clear evidence of principal-agent conflict. Surprisingly, the earlier GPT-3.5 model exhibits more nuanced behaviour in response to changes in information asymmetry, whereas the later GPT-4 model is more rigid in adhering to its prior alignment. Our results highlight the importance of incorporating principles from economics into the alignment process. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.11137&r=upt |
| By: | Daniele De Luca |
| Abstract: | The concept of power among players can be expressed as a combination of their utilities. A player who obeys another takes into account the utility of the dominant one. Technically it is a matter of superimposing some weighted sum or product function onto the individual utility function, where the weights can be represented through directed graphs that reflect a situation of power among the players. It is then possible to define some global indices of the system, such as the level of hierarchy, mutualism and freedom, and measure their effects on game equilibria. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.14170&r=upt |
| By: | Marcos Escobar-Anel; Yiyao Jiao |
| Abstract: | This paper proposes an expected multivariate utility analysis for ESG investors in which green stocks, brown stocks, and a market index are modeled in a one-factor, CAPM-type structure. This setting allows investors to accommodate their preferences for green investments according to proper risk aversion levels. We find closed-form solutions for optimal allocations, wealth and value functions. As by-products, we first demonstrate that investors do not need to reduce their pecuniary satisfaction in order to increase green investments. Secondly, we propose a parameterization to capture investors' preferences for green assets over brown or market assets, independent of performance. The paper uses the RepRisk Rating of U.S. stocks from 2010 to 2020 to select companies that are representative of various ESG ratings. Our empirical analysis reveals drastic increases in wealth allocation toward high-rated ESG stocks for ESG-sensitive investors; this holds even as the overall level of pecuniary satisfaction is kept unchanged. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.12161&r=upt |
| By: | V\'elez Jim\'enez; Rom\'an Alberto; Lecuanda Ontiveros; Jos\'e Manuel; Edgar Possani |
| Abstract: | This paper presents a novel approach for optimizing betting strategies in sports gambling by integrating Von Neumann-Morgenstern Expected Utility Theory, deep learning techniques, and advanced formulations of the Kelly Criterion. By combining neural network models with portfolio optimization, our method achieved remarkable profits of 135.8% relative to the initial wealth during the latter half of the 20/21 season of the English Premier League. We explore complete and restricted strategies, evaluating their performance, risk management, and diversification. A deep neural network model is developed to forecast match outcomes, addressing challenges such as limited variables. Our research provides valuable insights and practical applications in the field of sports betting and predictive modeling. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.13807&r=upt |
| By: | Ligon, Ethan |
| Abstract: | The hallmark of full risk sharing is that agents' marginal utilities of expenditure (MUEs) have a simple factor structure; a Pareto weight is divided by an aggregate price. Take logarithms and full risk-sharing can be easily tested using panel data with two-way fixed effects. The catch is that we don't directly observe MUEs, and must infer these using data on consumption expenditures. The standard approach to this inference problem is to assume some form of homothetic utility, in which case the MUE is a function of total expenditures and a single price index, and all demands have unit price elasticities. This approach works well when the shocks being tested affect agents' budgets without changing prices; i.e., when the shocks are idiosyncratic. But "covariate" shocks may change relative prices, in which case the standard risk-sharing tests which assume that no demands are inelastic will deliver apparently perverse results. What is the class of utility structures that allow one to test risk-sharing using only panel data on expenditures and two-way fixed effects, and does this class included non-homothetic preferences which are consistent with more realistic demand responses to changes in relative prices? We obtain this class, which happens to be semi-parametric and nests the usual homothetic specification, but which allows for highly flexible Engel curves, with $n$ parameters corresponding to the income elasticities of $n$ goods. We provide a simple algorithm to infer both these parameters and the agents' MUEs. We compute these using panel data from Uganda, and show that risk-sharing tests of covariate shocks using our computed MUEs deliver sensible results while the standard tests do not. |
| Keywords: | Social and Behavioral Sciences, Risk sharing, covariate shocks, Constant Frisch Elasticity demands, Uganda |
| Date: | 2023–07–28 |
| URL: | http://d.repec.org/n?u=RePEc:cdl:agrebk:qt2zr503fq&r=upt |
| By: | Florian Perusset (École Polytechnique Fédérale de Lausanne; Swiss Finance Institute); Michael Rockinger (University of Lausanne; and Swiss Finance Institute) |
| Abstract: | We consider a laboratory where bootstrapped synthetic structured products (convertible bonds, reverse convertibles, or barrier reverse convertibles) are added to a 60\% stock and 40\% bond portfolio. By using market data on the underlying assets which are stocks and bonds we directly inherit a realistic dynamic. We show that including structured products in the 60/40 portfolio results in a lower return and lower risk-adjusted performances regardless of what type of structured product is considered. Adding structured products to a portfolio impacts the distributional properties, rendering the distribution less Gaussian. By computing the opportunity costs of including structured products in the 60/40 portfolio, based on a Taylor approximation around the expected utility, we demonstrate that the opportunity cost is negative for all structured products and for reasonable levels of risk-aversion. This finding implies disutility for investors who choose to include structured products in their portfolio. For more complicated opaque structured products without explicit close-form solutions but with stale prices and transaction costs, we expect further performance deterioration. |
| Keywords: | Structured product portfolio performance, convertible bonds, reverse convertible, barrier reverse convertible |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp2347&r=upt |
| By: | Hamed Amini; Maxim Bichuch; Zachary Feinstein |
| Abstract: | Prediction markets allow traders to bet on potential future outcomes. These markets exist for weather, political, sports, and economic forecasting. Within this work we consider a decentralized framework for prediction markets using automated market makers (AMMs). Specifically, we construct a liquidity-based AMM structure for prediction markets that, under reasonable axioms on the underlying utility function, satisfy meaningful financial properties on the cost of betting and the resulting pricing oracle. Importantly, we study how liquidity can be pooled or withdrawn from the AMM and the resulting implications to the market behavior. In considering this decentralized framework, we additionally propose financially meaningful fees that can be collected for trading to compensate the liquidity providers for their vital market function. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.08768&r=upt |
| By: | Pashchenko, Svetlana; Porapakkarm, Ponpoje; Jang, Youngsoo |
| Abstract: | How should we compare welfare across pension systems in presence of differential mortality? A commonly used standard utilitarian criterion implicitly favors the long-lived over the short-lived. We investigate under what conditions this ranking is reversed. We clearly distinguish between the redistribution along mortality and income dimensions, and thus between mortality and income progressivity. We show that when mortality is independent of income, mortality progressivity can be optimal only when (i) there is more aversion to inequality in lifetime utilities compared to aversion to consumption inequality, (ii) life is valuable. When the short-lived tend to have lower income, mortality progressivity can be also optimal when income redistribution tools are limited. In this case, mortality progressivity is used to substitute for income progressivity. |
| Keywords: | Mortality-related redistribution, Pensions, Social Security, Annuities, Life-Cycle Model |
| JEL: | G22 H21 H55 I38 |
| Date: | 2023–07–14 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:117936&r=upt |
| By: | Kopsacheilis, Orestis (Technical University of Munich); Goerg, Sebastian J. (Technische Universität München) |
| Abstract: | Having an accurate account of preferences help governments design better policies for their citizens, organizations develop more efficient incentive schemes for their employees and adjust their product to better suit their clients' needs. The plethora of elicitation methods most commonly used can be broadly distinguished between methods that rely on people self-assessing and directly stating their preferences (qualitative) and methods that are indirectly inferring such preferences through choices in some task (quantitative). Alarmingly, the two approaches produce systematically different conclusions about preferences and, therefore, survey designers often include both quantitative and qualitative items. An important methodological question that is hitherto unaddressed is whether the order in which quantitative and qualitative items are encountered affects elicited preferences. We conduct three, pre-registered, studies with a total of 3, 000 participants, where we elicit preferences about risk, time-discounting and altruism in variations of two conditions: 'Quantitative First' and 'Qualitative First'. We find significant and systematic order effects. Eliciting preferences through qualitative items first boosts inferred patience and altruism while using quantitative items first increases the cross-method correlation for risk and time preferences. We explore how monetary incentivization and introducing financial context modulates these results and discuss the implications of our findings in the context of nudging interventions as well as our understanding of the nature of preferences. |
| Keywords: | preferences, qualitative vs. quantitative measures, risk, altruism, patience |
| JEL: | C83 C91 D01 D91 |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp16343&r=upt |
| By: | Frank Kleibergen; Lingwei Kong |
| Abstract: | We propose identification robust statistics for testing hypotheses on the risk premia in dynamic affine term structure models. We do so using the moment equation specification proposed for these models in Adrian et al. (2013). We extend the subset (factor) Anderson-Rubin test from Guggenberger et al. (2012) to models with multiple dynamic factors and time-varying risk prices. Unlike projection-based tests, it provides a computationally tractable manner to conduct identification robust tests on a larger number of parameters. We analyze the potential identification issues arising in empirical studies. Statistical inference based on the three-stage estimator from Adrian et al. (2013) requires knowledge of the factors' quality and is misleading without full-rank beta's or with sampling errors of comparable size as the loadings. Empirical applications show that some factors, though potentially weak, may drive the time variation of risk prices, and weak identification issues are more prominent in multi-factor models. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.12628&r=upt |