Probability Of Payoff Research Articles

Probability discounting and money pumps

AbstractIn response to cases that involve tiny probabilities of huge payoffs, some argue that we ought to discount small probabilities down to zero. However, this paper shows that doing so violates Independence and Continuity, and as a result of these violations, those who discount small probabilities can be exploited by money pumps. Various possible ways of avoiding exploitation will be discussed. This paper concludes that the money pump for Independence undermines the plausibility of discounting small probabilities. Much of the discussion on Independence generalizes to other views that also violate Independence.

On skew preference or non-skew preference of a CPT DM revealed in lottery choices with three payoffs

In this letter we illustrate that the representative Cumulative Prospect Decision Maker when choosing between lotteries with three payoffs that exhibit the same probabilities of payoffs and expected return and variance can exhibit either skew preference or non-skew preference and consequently explain the conflicting experimental result reported in the literature.

Risk and ambiguity aversion: Incentives or disincentives for adoption of improved agricultural land management practices?

AbstractFarmers grapple with uncertainties related to the adoption of improved agricultural practices. Adoption decisions on these practices may vary in response to risk in which farmers may be able to predict the chances of occurrence on outcomes of their decisions, and/or ambiguity where adoption‐decision outcome probabilities are unknown. Also, these uncertainties may emanate from imperfect information on production returns from adoption and adoption‐related fixed costs. In this paper, we study whether risk and ambiguity aversion create incentives or disincentives for intensity and duration of adoption of improved agricultural practices. For this, we combine experimental with survey data. We find that ambiguity aversion reduces incentives for high‐intensity adoption while risk aversion attenuates this disincentive. As expected, risk aversion increases incentives for longer adoption of improved agricultural practices. Experience was expected to allow farmers to learn enough about payoff probabilities from adoption and render ambiguity aversion less important. Yet, we find it reduces the duration of adoption of soil and water conservation structures, which could be explained by adoption‐related high fixed costs. On the other hand, ambiguity aversion appears to matter little with adoption of agroforestry despite the associated high fixed and management costs attributed to integrated agri‐silviculture and agro‐silvopastoral systems. Given the complementary nature of the practices, agricultural policy should be directed at interventions that attenuate the deterrent effect of ambiguity aversion through providing information related to production returns from the adoption of improved practices that involve high fixed (management) costs.

The epistemic challenge to longtermism

Longtermists claim that what we ought to do is mainly determined by how our actions might affect the very long-run future. A natural objection to longtermism is that these effects may be nearly impossible to predict—perhaps so close to impossible that, despite the astronomical importance of the far future, the expected value of our present actions is mainly determined by near-term considerations. This paper aims to precisify and evaluate one version of this epistemic objection to longtermism. To that end, I develop two simple models for comparing ‘longtermist’ and ‘neartermist’ interventions, incorporating the idea that it is harder to make a predictable difference to the further future. These models yield mixed conclusions: if we simply aim to maximize expected value, and don’t mind premising our choices on minuscule probabilities of astronomical payoffs, the case for longtermism looks robust. But on some prima facie plausible empirical worldviews, the expectational superiority of longtermist interventions depends heavily on these ‘Pascalian’ probabilities. So the case for longtermism may depend either on plausible but non-obvious empirical claims or on a tolerance for Pascalian fanaticism.

Health shocks and mortgage debt payoff among American homeowners over age 50: A survival analysis

AbstractMortgage debt is financially burdensome for many older homeowners in the United States. As people age, declining health can bring about increased healthcare costs. Focusing on homeowners aged 50 and older in the U.S., we investigate two research questions: (1) To what extent does a heath shock affect the likelihood of paying off a mortgage voluntarily or involuntarily? and (2) how long does a health shock delay the time it takes to pay off a mortgage? We used eight biannual waves (2004–2018) of the Health and Retirement Study containing 11,772 borrowers to build survival regression models. Results showed that a health shock reduced the likelihood of voluntary payoff by 12%, while it increased the probability of involuntary payoff by 18%. A health shock delayed voluntary and involuntary payoffs for 30 and 21 months, respectively. We discuss tax deduction and HELOCs as strategies to reduce older homeowners' mortgage strain.

Rentabilidad financiero-fiscal de las rentas de jubilación temporales o vitalicias aseguradas y contratadas a prima única

El objetivo de este trabajo es determinar la rentabilidad financiero-fiscal que puede obtener un asegurado al contratar una renta de supervivencia diferida y vitalicia. Se obtienen las expresiones analíticas de la distribución de probabilidad de la rentabilidad real de la operación, de la rentabilidad esperada y de los indicadores de riesgo que proponemos utilizar junto a esta rentabilidad. Se desarrolla una aplicación numérica de un caso particular de forma que el estudio realizado muestra la aplicabilidad de los resultados obtenidos permitiendo al asegurado tomar sus decisiones en ambiente aleatorio con la máxima información.

Stakes and expertise modulate conformity in economic choice

The influences of expertise and group size on an individual’s tendency to align with a majority opinion have been attributed to informational and normative conformity, respectively: Whereas the former refers to the treatment of others’ decisions as proxies for outcomes, the latter involves positive affect elicited by group membership. In this study, using a social gambling task, we pitted alignment with a high- vs. low-expertise majority against a hypothetical monetary reward, thus relating conformity to a broader literature on valuation and choice, and probed the countering influence of a high-expertise minority opinion. We found that the expertise of a countering minority group significantly modulated alignment with a low-expertise majority, but only if such alignment did not come at a cost. Conversely, participants’ knowledge of payoff probabilities predicted the degree of majority alignment only when a high-expertise majority endorsed a more costly option. Implications for the relative influences of expertise and stakes on conformity are discussed.

Constantly timing, but not always controlled by time: Evidence from the midsession reversal task.

We used a midsession reversal task to investigate how temporal and situational cues may combine to determine choice in frequently changing environments. Pigeons learned a simultaneous discrimination with 2 stimuli: S1 and S2. Choices of S1 were reinforced only during the first trials, and choices of S2 were reinforced only during the last trials of the session, that is, the reinforcement contingencies reversed once during the session. To weaken the temporal cue (time into the session) that signaled the reversal trial, we varied the location of reversal trial randomly across sessions; to weaken the situational cue (the outcome of the previous trials that might support a win-stay/loose shift strategy), we varied the payoff probabilities associated with S1 and S2. Performance was consistent neither with the exclusive use of a timing strategy, nor with the exclusive use of a situational, win-stay/lose-shift strategy. Instead, choice seemed to be under joint control of both cues. The relative influence of these cues was dynamic: When payoff was higher for S1 than S2, behavior was less time-controlled than when the payoff was higher for S2 that S1, or when they were equal. We advance a descriptive mixture model of joint control for the midsession reversal task. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Stochastic Asymmetric Blotto Game Approach for Wireless Resource Allocation Strategies

The development of modellings and analytical tools to structurise and study the allocation of resources through noble user competitions become essential, especially considering the increased degree of heterogeneity in application and service demands that will be cornerstone in future communication systems. Stochastic asymmetric Blotto games appear promising to modelling such problems, and devising their Nash equilibrium (NE) strategies by anticipating the potential outcomes of user competitions. In this regard, this paper approaches the generic energy efficiency problem with a new stochastic asymmetric Blotto game paradigm to enable the derivation of joint optimal bandwidth and transmit power allocations by setting multiple users to compete in multiple auction-like contests for their individual resource demands. The proposed modelling innovates by abstracting the notion of fairness from centrally-imposed to distributed-competitive, where each user’s pay-off probability is expressed as quantitative bidding metric, so as, all users’ actions can be interdependent, i.e., each user attains its utility given the allocations of other users, which eliminates the chance of low-valued carriers not being claimed by any user, and, in principle, enables the full utilisation of wireless resources. We also contribute by resolving the allocation problem with low complexity using new mathematical techniques based on Charnes-Cooper transformation, which eliminate the additional coefficients and multipliers that typically appear during optimisation analysis, and derive the joint optimal strategy as a set of linear single-variable functions for each user. We prove that our strategy converges towards a unique, monotonous and scalable NE, and examine its optimality, positivity and feasibility properties in detail. Simulation comparisons with relevant studies confirm the superiority of our approach in terms of higher energy efficiency performance, fairness index and quality-of-service provision.

Optimal foraging and the information theory of gambling.

At a macroscopic level, part of the ant colony life cycle is simple: a colony collects resources; these resources are converted into more ants, and these ants in turn collect more resources. Because more ants collect more resources, this is a multiplicative process, and the expected logarithm of the amount of resources determines how successful the colony will be in the long run. Over 60 years ago, Kelly showed, using information theoretic techniques, that the rate of growth of resources for such a situation is optimized by a strategy of betting in proportion to the probability of pay-off. Thus, in the case of ants, the fraction of the colony foraging at a given location should be proportional to the probability that resources will be found there, a result widely applied in the mathematics of gambling. This theoretical optimum leads to predictions as to which collective ant movement strategies might have evolved. Here, we show how colony-level optimal foraging behaviour can be achieved by mapping movement to Markov chain Monte Carlo (MCMC) methods, specifically Hamiltonian Monte Carlo (HMC). This can be done by the ants following a (noisy) local measurement of the (logarithm of) resource probability gradient (possibly supplemented with momentum, i.e. a propensity to move in the same direction). This maps the problem of foraging (via the information theory of gambling, stochastic dynamics and techniques employed within Bayesian statistics to efficiently sample from probability distributions) to simple models of ant foraging behaviour. This identification has broad applicability, facilitates the application of information theory approaches to understand movement ecology and unifies insights from existing biomechanical, cognitive, random and optimality movement paradigms. At the cost of requiring ants to obtain (noisy) resource gradient information, we show that this model is both efficient and matches a number of characteristics of real ant exploration.

On the Possibility of Informative Equilibria in Futures Markets with Feedback

AbstractWe study the existence of equilibria and the information content of prices in futures markets where the probability of future payoffs can be altered by an intervening agent who acts in response to the market price, hence creating a feedback effect. We focus on the market with the simplest possible structure: traders betting on the occurrence of a future event by buying or selling Arrow-Debreu securities (one dollar claims contingent on a binary outcome). We find that in the presence of feedback: (i) a rational expectations equilibrium may not exist; (ii) the market price may decline in response to information that is ex-ante more favorable to the occurrence of the underlying event; (iii) an equilibrium that reveals no information may obtain. Thus, feedback from an intervening agent materially alters the way in which price responds to information, and potentially undermines the viability of the market itself.

Biasing performance through differential payoff in a temporal bisection task.

We investigated how differential payoffs affect temporal discrimination. In a temporal bisection task, pigeons learned to choose one key after a short sample and another key after a long sample. When presented with a range of intermediate samples they produced a Gaussian psychometric function characterized by a location (bias) parameter and a scale (sensitivity) parameter. When one key yielded more reinforcers than the other, the location parameter changed, with the pigeons biasing their choices toward the richer key. We then reproduced the bisection task in a long operant chamber, with choice keys far apart, and tracked the pigeons' motion patterns during the sample. These patterns were highly stereotypical-on the long sample trials, the pigeons approached the short key at sample onset, stayed there for a while, and then departed to the long key. The distribution of departure times also was biased when the payoff probabilities differed. Moreover, it is likely that temporal control decreased while control by location increased. No evidence was found of changes in temporal sensitivity. The results are consistent with models of timing that take into account bias effects and competition of stimulus control. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Refined expected value decision rules

We consider the difficult problem of choosing between alternatives where the payoffs for the alternatives are uncertain and modeled via discrete probability distributions. One popular approach for making a choice in this complex environment is to use the idea of expected value; we prefer alternatives with larger expected value. Here we suggest an approach for refining the calculation of the expected value to allow for the inclusion of a requirement that we prefer an alternative with payoff probability distribution P1 to an alternative with payoff probability distribution P2 by assuring that expected value of P1 is larger then the expected value of P2.

Stock return anomalies and individual investors in the Korean stock market

I find a negative cross-sectional relation between the probability of future price crashes and subsequent returns in the Korean stock market, substantially due to the overpricing of stocks with a high probability of crashes. Using precise information on retail trading in the Korean stock market, I also find that stocks with a high crash probability have a relatively high proportion of retail trading. Moreover, the negative relation between the probability of crashes and stock returns is much stronger in stocks traded more heavily by retail investors. However, I cannot find a negative relation between the probability of jackpot payoffs and subsequent returns in Korea, unlike in the United States, even among stocks with a high proportion of retail trading. Both portfolio- and firm-level evidence on the crash effect suggests that stocks with a higher retail trading proportion are more likely to be overpriced, as expected from the limits to arbitrage literature.

A Finite Memory Automaton for Two-Armed Bernoulli Bandit Problems

Existing approaches to the multi-armed bandit (MAB) primarily rely on perfect recall of past actions to generate estimates for arm payoff probabilities; it is further assumed that the decision maker knows whether arm payoff probabilities can change. To capture the computational limitations many decision making systems face, we explore performance under bounded resources in the form of imperfect recall of past information. We present a finite memory automaton (FMA) designed to solve static and dynamic MAB problems. The FMA demonstrates that an agent can learn a low regret strategy without knowing whether arm payoff probabilities are static or dynamic and without having perfect recall of past actions. Roughly speaking, the automaton works by maintaining a relative ranking of arms rather than estimating precise payoff probabilities.

Theoretical Behaviorism, Economic Theory, and Choice

Choice behavior is studied differently in humans and in animals, and different theories have arisen to explain the results. I suggest that an approach derived from animal studies is also appropriate for human choice. Daniel Kahneman and Amos Tversky's prospect theory, a popular two-part account of human choice, is a functional theory amounting, after some years of evolution, to a classification of types of deviation from “rational” reward maximization. Animal choice, on the other hand, can be explained causally as the outcome of competition between a set of possible responses with different “strengths.” The strength of each response is directly related to its historical payoff probability, and responses compete in winner-take-all fashion. An “active” response occurs and is strengthened or weakened depending on its outcome. If it is sufficiently weakened, it will be supplanted by the strongest “silent” response. This cumulative effects (CE) model has been tested in operant conditioning experiments that show, for example, that when choosing between two identical probabilistic choices in a “two-armed bandit” situation, animals will fixate on one if the payoff probabilities are high, but be indifferent if they are low, a pattern not easily deducible from any kind of optimality theory. Kahneman's distinction between “fast” and “slow” systems is indistinguishable from the distinction between active and silent responses in the CE model, which therefore offers a causal account of human as well as animal choice behavior.

Financial contagion and asset pricing

Asset market interconnectedness can give rise to significant contagion risks during periods of financial crises that extend beyond the risks associated with changes in volatilities and correlations. These channels include the transmission of shocks operating through changes in the higher order comoments of asset returns, including changes in coskewness arising from changes in the interaction between volatility and average returns across asset markets. These additional contagion channels have nontrivial implications for the pricing of options through changes in the payoff probability structure and more generally, in the management of financial risks. The effects of incorrectly pricing risk has proved to be significant during many financial crises, including the subprime crisis from mid 2007 to mid 2008, the Great Recession beginning 2008 and the European debt crisis from 2010. Using an exchange options model, the effects of changes in the comoments of asset returns across asset markets are investigated with special emphasis given to understanding the effects on hedging risk during financial crises. The results reveal that by not correctly pricing the risks arising from higher order moments during financial crises, there is significant mispricing of options, while hedged portfolios during noncrisis periods become exposed to price movements in times of crises.

Effects of Response Frequency Constraints on Learning in a Non-Stationary Multi-armed Bandit Task

An n-armed bandit task was used to investigate the trade-off between exploratory (choosing lesser-known options) and exploitive (choosing options with the greatest known probability of reinforcement) human choice in a trial-and-error learning problem. A different probability of reinforcement was assigned to each of eight response options using random-ratios (RRs), and participants chose by clicking buttons in a circular display on a computer screen using a computer mouse. To differentially increase exploration, relative frequency thresholds were randomly assigned to each participant and acted as task constraints limiting the proportion of total responses that could be attributed to any response option. The potential benefit of increased exploration in non-stationary environments was investigated by changing payoff probabilities so that the leanest options became the richest or the richest options became the leanest. On the average, forcing participants to explore at moderate to high levels always resulted in their earning less reinforcement, even when the payoffs changed. This outcome may be due to humans’ natural level of exploration in our task being sufficiently high to create sensitivity to environmental dynamics.

Financial Contagion and Asset Pricing

Asset market interconnectedness can give rise to significant contagion risks during periods of financial crises that extend beyond the risks associated with changes in volatilities and correlation. These channels include the transmission of shocks operating through changes in the higher order co-moments of asset returns, including changes in co-skewness arising from changes in the interaction between volatility and average returns across asset markets. These additional contagion channels have nontrivial implications for the pricing of options through changes in the payoff probability structure and more generally, in the management of financial risks. The effects of incorrectly pricing risk has proved to be significant during many financial crises, including the sub-prime crisis from mid 2007 to mid 2008, the Great Recession beginning 2008 and the European debt crisis from 2010. Using an exchange options model, the effects of changes in the co-moments of asset returns across asset markets are investigated with special emphasis given to understanding the effects on hedging risk during financial crises. The results reveal that by not correctly pricing the risks arising from higher order moments during financial crises, there is significant mis-pricing of options, while hedged portfolios during non-crisis periods become exposed to price movements in times of crises.

Hedge Funds and Chapter 11

ABSTRACTThis paper studies the presence of hedge funds in the Chapter 11 process and their effects on bankruptcy outcomes. Hedge funds strategically choose positions in the capital structure where their actions could have a bigger impact on value. Their presence, especially as unsecured creditors, helps balance power between the debtor and secured creditors. Their effect on the debtor manifests in higher probabilities of the latter's loss of exclusive rights to file reorganization plans, CEO turnover, and adoptions of key employee retention plan, while their effect on secured creditors manifests in higher probabilities of emergence and payoffs to junior claims.