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on Utility Models and Prospect Theory |
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Issue of 2024‒01‒22
thirteen papers chosen by |
| By: | Eric André (EM - emlyon business school); Antoine Bommier; François Le Grand (EM - emlyon business school) |
| Abstract: | We analyze the impact of risk aversion and ambiguity aversion on the competing demands for annuities and bequeathable savings using a lifecycle recursive utility model. Our main finding is that risk aversion and ambiguity aversion have similar effects: an increase in either of the two reduces annuity demand and enhances bond holdings. We obtain this unequivocal result in the flexible intertemporal framework of Hayashi and Miao (2011) by assuming that the agent's preferences are monotone with respect to first-order stochastic dominance. Our contribution is then twofold. First, from a decision-theoretic point of view, we show that monotonicity allows one to obtain clear-cut results about the respective roles of risk and ambiguity aversion. Second, from the insurance point of view, our result that the demand for annuities decreases with risk and ambiguity aversion stands in contrast with what is usually found with other insurance products. As such, it may help explain the low annuitization level observed in the data. |
| Keywords: | Recursive utility, Lifecycle model, Ambiguity aversion, Risk aversion, Saving choices, Annuity puzzle |
| Date: | 2022–08–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-04325572&r=upt |
| By: | Mehmet S. Ismail; Ronald Peeters |
| Abstract: | It is well known that ex ante social preferences and expected utility are not always compatible. In this note, we introduce a novel framework that naturally separates social preferences from selfish preferences to answer the following question: What specific forms of social preferences can be accommodated within the expected utility paradigm? In a departure from existing frameworks, our framework reveals that ex ante social preferences are not inherently in conflict with expected utility in games, provided a decision-maker's aversion to randomization in selfish utility "counterbalances" her social preference for randomization. We also show that when a player's preferences in both the game (against another player) and the associated decision problem (against Nature) conform to expected utility axioms, the permissible range of social preferences becomes notably restricted. Only under this condition do we reaffirm the existing literature's key insight regarding the incompatibility of ex ante inequality aversion with expected utility. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.06048&r=upt |
| By: | Sven Neth |
| 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. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.09796&r=upt |
| By: | Zongxia Liang; Keyu Zhang |
| Abstract: | In this paper we study a time-inconsistent portfolio optimization problem for competitive agents with CARA utilities and non-exponential discounting. The utility of each agent depends on her own wealth and consumption as well as the relative wealth and consumption to her competitors. Due to the presence of a non-exponential discount factor, each agent's optimal strategy becomes time-inconsistent. In order to resolve time-inconsistency, each agent makes a decision in a sophisticated way, choosing open-loop equilibrium strategy in response to the strategies of all the other agents. We construct explicit solutions for the $n$-agent games and the corresponding mean field games (MFGs) where the limit of former yields the latter. This solution is unique in a special class of equilibria. As a by-product, we find that competition in the time-inconsistency scenario modifies the agent's risk tolerance as it does in the time-consistent scenario. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.14437&r=upt |
| By: | Anton Kolotilin (School of Economics, UNSW); Roberto Corrao (Department of Economics, MIT); Alexander Wolitzky (Department of Economics, MIT) |
| Abstract: | In persuasion problems where the receiver’s utility is single-peaked in a one-dimensional action, optimal signals are characterized by duality, based on a first-order approach to the receiver’s problem. A signal that pools at most two states in each realization is always optimal, and such pairwise signals are the only solutions under a non-singularity condition on utilities (the twist condition). Our core results provide conditions under which higher actions are induced at more or less extreme pairs of states, so that the induced action is single-dipped or single-peaked on each set of nested pairs of states. We also provide conditions for the optimality of either full disclosure or negative assortative disclosure, where signal realizations can be ordered from least to most extreme. Methodologically, our proofs rely on a novel complementary slackness theorem for persuasion problems. |
| Keywords: | persuasion, information design, duality, optimal transport, first-order approach, pairwise signals, twist condition, single-dipped disclosure, negative assortative disclosure, complementary slackness |
| JEL: | C78 D82 D83 |
| Date: | 2023–02 |
| URL: | http://d.repec.org/n?u=RePEc:swe:wpaper:2023-07&r=upt |
| By: | Japneet Kaur (Indira Gandhi Institute of Development Research) |
| Abstract: | In an economy with club goods, we introduce the concept of von Neumann-Morgensetern stable sets. Our main result provides a correspondence between stable sets of a club economy comprising a continuum of agents and finitely many types with those that form in the related finite economy. Along with the trade in private goods, agents in our economy can belong to multiple clubs. A club is characterised by the undertaking in which it is engaged and the external attributes of its members. Further, inspired by Harsanyi [10], we also bring in the notion of `sophisticated stability' and show an equivalence between `sophisticated stable sets' in the utility space with those that form in the allocation space. |
| Keywords: | Club goods, Stable sets of allocations, Stable sets of payoffs, Core, Sophisticated stability |
| JEL: | D50 D51 D60 D61 D71 |
| Date: | 2023–11 |
| URL: | http://d.repec.org/n?u=RePEc:ind:igiwpp:2023-011&r=upt |
| By: | Min Dai; Yuchao Dong; Yanwei Jia; Xun Yu Zhou |
| Abstract: | We study Merton's expected utility maximization problem in an incomplete market, characterized by a factor process in addition to the stock price process, where all the model primitives are unknown. We take the reinforcement learning (RL) approach to learn optimal portfolio policies directly by exploring the unknown market, without attempting to estimate the model parameters. Based on the entropy-regularization framework for general continuous-time RL formulated in Wang et al. (2020), we propose a recursive weighting scheme on exploration that endogenously discounts the current exploration reward by the past accumulative amount of exploration. Such a recursive regularization restores the optimality of Gaussian exploration. However, contrary to the existing results, the optimal Gaussian policy turns out to be biased in general, due to the interwinding needs for hedging and for exploration. We present an asymptotic analysis of the resulting errors to show how the level of exploration affects the learned policies. Furthermore, we establish a policy improvement theorem and design several RL algorithms to learn Merton's optimal strategies. At last, we carry out both simulation and empirical studies with a stochastic volatility environment to demonstrate the efficiency and robustness of the RL algorithms in comparison to the conventional plug-in method. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.11797&r=upt |
| By: | Fangzhi Wang; Hua Liao; Richard S. J. Tol; Changjing Ji |
| Abstract: | Carbon abatement decisions are usually based on the implausible assumption of constant social preference. This paper focuses on a specific case of market and non-market goods, and investigates the optimal climate policy when social preference for them is also changed by climate policy in the DICE model. The relative price of non-market goods grows over time due to increases in both relative scarcity and appreciation of it. Therefore, climbing relative price brings upward the social cost of carbon denominated in terms of market goods. Because abatement decision affects the valuation of non-market goods in the utility function, unlike previous climate-economy models, we solve the model iteratively by taking the obtained abatement rates from the last run as inputs in the current run. The results in baseline calibration advocate a more stringent climate policy, where endogenous social preference to climate policy raises the social cost of carbon further by roughly 12%-18% this century. Moreover, neglecting changing social preference leads to an underestimate of non-market goods damages by 15%. Our results support that climate policy is self-reinforced if it favors more expensive consumption type. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.11010&r=upt |
| By: | Pierfrancesco Guarino |
| Abstract: | Given a dynamic ordinal game, we deem a strategy sequentially rational if there exist a Bernoulli utility function and a conditional probability system with respect to which the strategy is a maximizer. We establish a complete class theorem by characterizing sequential rationality via the new Conditional B-Dominance. Building on this notion, we introduce Iterative Conditional B-Dominance, which is an iterative elimination procedure that characterizes the implications of forward induction in the class of games under scrutiny and selects the unique backward induction outcome in dynamic ordinal games with perfect information satisfying a genericity condition. Additionally, we show that Iterative Conditional B-Dominance, as a `forward induction reasoning' solution concept, captures: $(i)$ the unique backward induction outcome obtained via sophisticated voting in binary agendas with sequential majority voting; $(ii)$ farsightedness in dynamic ordinal games derived from social environments; $(iii)$ a unique outcome in ordinal Money-Burning Games. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.03536&r=upt |
| By: | Charlotte Cordes (LMU Munich); Jana Friedrichsen (Kiel University, CESifo); Simeon Schudy (Ulm University, CESifo) |
| Abstract: | Traditionally, economic models have attributed procrastination to present bias. However, procrastination may also arise when individuals derive anticipatory utility from holding motivated, overly optimistic beliefs about the workload they need to complete. This study provides a rigorous empirical test for this notion of `motivated procrastination'. In a longitudinal experiment over four weeks, individuals have to complete a cumbersome task of unknown length. They are exposed to exogenous variation in i) their expectation regarding their workload and ii) scope for motivated reasoning. We find that scope for motivated reasoning allows workers to hold substantially more optimistic beliefs and identify a causal link between the exogenous variation in beliefs and the deferral of work to the future. This systematic belief-based delay of work (motivated procrastination) turns out to be robust to accounting for decision-makers' time preferences and emotional responses, and looms largest for decision makers who tend to not acquire information that may include negative news. |
| Keywords: | anticipatory utility; beliefs; memory; motivated cognition; procrastination; real effort; task allocation; |
| JEL: | C91 D83 D84 D90 D91 |
| Date: | 2023–12–03 |
| URL: | http://d.repec.org/n?u=RePEc:rco:dpaper:471&r=upt |
| By: | Benjamin Avanzi; Lewis de Felice |
| Abstract: | A retiree's appetite for risk is a common input into the lifetime utility models that are traditionally used to find optimal strategies for the decumulation of retirement savings. In this work, we consider a retiree with potentially differing appetites for the key financial risks of decumulation. We set out to determine whether these differing risk appetites have a significant impact on the retiree's optimal choice of strategy. To do so, we design and implement a framework which selects the optimal decumulation strategy from a general set of admissible strategies in line with a retiree's goals, and under differing appetites for the key risks of decumulation. Overall, we find significant evidence to suggest that a retiree's differing appetites for different decumulation risks will impact their optimal choice of strategy at retirement. Through an illustrative example calibrated to the Australian context, we find results which are consistent with actual behaviours in this jurisdiction (in particular, a shallow market for annuities), which lends support to our framework and may provide some new insight into the so-called annuity puzzle. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.14355&r=upt |
| By: | Francesco Cesarone; Massimiliano Corradini; Lorenzo Lampariello; Jessica Riccioni |
| Abstract: | We focus on a behavioral model, that has been recently proposed in the literature, whose rational can be traced back to the Half-Full/Half-Empty glass metaphor. More precisely, we generalize the Half-Full/Half-Empty approach to the context of positive and negative lotteries and give financial and behavioral interpretations of the Half-Full/Half-Empty parameters. We develop a portfolio selection model based on the Half-Full/Half-Empty strategy, resulting in a nonconvex optimization problem, which, nonetheless, is proven to be equivalent to an alternative Mixed-Integer Linear Programming formulation. By means of the ensuing empirical analysis, based on three real-world datasets, the Half-Full/Half-Empty model is shown to be very versatile by appropriately varying its parameters, and to provide portfolios displaying promising performances in terms of risk and profitability, compared with Prospect Theory, risk minimization approaches and Equally-Weighted portfolios. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.10749&r=upt |
| By: | Roberto Daluiso; Marco Pinciroli; Michele Trapletti; Edoardo Vittori |
| Abstract: | This work studies the dynamic risk management of the risk-neutral value of the potential credit losses on a portfolio of derivatives. Sensitivities-based hedging of such liability is sub-optimal because of bid-ask costs, pricing models which cannot be completely realistic, and a discontinuity at default time. We leverage recent advances on risk-averse Reinforcement Learning developed specifically for option hedging with an ad hoc practice-aligned objective function aware of pathwise volatility, generalizing them to stochastic horizons. We formalize accurately the evolution of the hedger's portfolio stressing such aspects. We showcase the efficacy of our approach by a numerical study for a portfolio composed of a single FX forward contract. |
| Date: | 2023–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2312.14044&r=upt |