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on Utility Models and Prospect Theory |
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Issue of 2022‒05‒09
eleven papers chosen by |
| By: | Hammond, Peter J. (Dept. of Economics, University of Warwick) |
| Abstract: | Following previous work on consequentialist decision theory, we consider an unrestricted domain of finite decision trees, including continuation subtrees, with : (i) decision nodes where the decision maker must make a move ; (ii) chance nodes at which a “roulette lottery†with exogenously specified strictly positive probabilities is resolved ; (iii) event nodes at which a “horse lottery†is resolved. A complete family of binary conditional base preference relations over Anscombe–Aumann lottery consequences is defined to be “prerational†just in case there exists a behaviour rule that is defined throughout the tree domain which is explicable as avoiding, under all predictable circumstances, consequences that are regrettable given what is feasible. Prerationality is shown to hold if and only if all conditional base preference relations are complete and transitive, while also satisfying both the independence axiom of expected utility theory and a strict form of Anscombe and Aumann’s extension of Savage’s sure thing principle. Assuming that the base relations satisfy non-triviality and a generalized form of state independence that holds even when consequence domains are state dependent, prerationality combined with continuity on Marschak triangles is equivalent to representation by a refined subjective expected utility function that excludes zero probabilities. |
| Keywords: | Prerational base relations ; rational planning ; decision trees ; regrettable consequences ; Anscombe–Aumann lotteries ; preference ordering ; independence axiom ; sure-thing principle ; subjective probability ; subjective expected utility ; Bayesian rationality ; state independence JEL codes: D81 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:wcreta:72&r= |
| By: | AZILLA, HANUM |
| Abstract: | Ilmu ekonomi (economics) adalah bagian ilmu sosial yang mempelajari bagaimana manusia menentukan pilihan dalam menggunakan sumber daya (resources) untuk menghasilkan benda (commodity) yang mereka butuhkan dalam hidup mereka agar memperoleh guna/manfaat (utility) yang sebesar-besarnya. |
| Date: | 2022–03–20 |
| URL: | http://d.repec.org/n?u=RePEc:osf:osfxxx:5t7fm&r= |
| By: | Anthropelos, Michail; Kardaras, Constantinos; Vichos, Georgios |
| Abstract: | We consider thin incomplete financial markets, where traders with heterogeneous preferences and risk exposures have motive to behave strategically regarding the demand schedules they submit, thereby impacting prices and allocations. We argue that traders relatively more exposed to the market portfolio tend to behave in a more risk tolerant manner. Noncompetitive equilibrium prices and allocations result as an outcome of a game among traders. General sufficient conditions for existence and uniqueness of such equilibrium are provided, with extensive analysis of two-trader transactions. Even though strategic behavior causes inefficient social allocations, traders with sufficiently high risk tolerance and/or high initial exposure to tradable securities obtain more utility gain in the noncompetitive equilibrium, when compared to the competitive one. |
| Keywords: | Nash equilibrium; effective risk aversion; noncompetitive risk sharing; price impact; thin markets |
| JEL: | F3 G3 |
| Date: | 2020–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:102275&r= |
| By: | Jingtang Ma; Zhengyang Lu; Zhenyu Cui |
| Abstract: | In this paper, we propose a new approach for stochastic control problems arising from utility maximization. The main idea is to directly start from the dynamical programming equation and compute the conditional expectation using a novel representation of the conditional density function through the Dirac Delta function and the corresponding series representation. We obtain an explicit series representation of the value function, whose coefficients are expressed through integration of the value function at a later time point against a chosen basis function. Thus we are able to set up a recursive integration time-stepping scheme to compute the optimal value function given the known terminal condition, e.g. utility function. Due to tensor decomposition property of the Dirac Delta function in high dimensions, it is straightforward to extend our approach to solving high-dimensional stochastic control problems. The backward recursive nature of the method also allows for solving stochastic control and stopping problems, i.e. mixed control problems. We illustrate the method through solving some two-dimensional stochastic control (and stopping) problems, including the case under the classical and rough Heston stochastic volatility models, and stochastic local volatility models such as the stochastic alpha beta rho (SABR) model. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.12745&r= |
| By: | Nick Netzer; Arthur Robson; Jakub Steiner; Pavel Kocourek |
| Abstract: | In a model inspired by neuroscience, we show that constrained optimal perception encodes lottery rewards using an S-shaped encoding function and over-samples low-probability events. The implications of this perception strategy for behavior depend on the decision-maker’s understanding of the risk. The strategy does not distort choice in the limit as perception frictions vanish when the decision-maker fully understands the decision problem. If, however, the decision-maker underrates the complexity of the decision problem, then risk attitudes reflect properties of the perception strategy even for vanishing perception frictions. The model explains adaptive risk attitudes and probability weighting as in prospect theory and, additionally, predicts that risk attitudes are strengthened by time pressure and attenuated by anticipation of large risks. |
| Keywords: | endogenous preferences, probability distortions, misspecified learning |
| JEL: | D81 D87 D91 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_9547&r= |
| By: | Juan Carlos Hatchondo (University of Western Ontario); Leonardo Martinez (IMF); Francisco Roch (IMF) |
| Abstract: | Using a quantitative sovereign default model, we characterize constrained efficient borrowing by a Ramsey government that commits to income-history-contingent borrowing paths taking as given ex-post optimal future default decisions. The Ramsey government improves upon the Markov government because it internalizes the effects of borrowing decisions in period t on borrowing opportunities prior to t. We show the effect of borrowing decisions in t on utility flows prior to t can be encapsulated by two single dimensional variables. Relative to a Markov government, the Ramsey government distorts borrowing decisions more when bond prices are more sensitive to borrowing, and changes in bond prices have a larger effect on past utility. In a quantitative exercise, more than 80% of the default risk is eliminated by a Ramsey government, without decreasing borrowing. The Ramsey government also has a higher probability of completing a successful deleveraging (without defaulting), while smoothing out the fiscal consolidation. |
| Keywords: | Sovereign Default, Long-term Debt, Time Inconsistency, Dbt Dilution, Deleveraging, Austerity, Debt Management, Fiscal Rules |
| JEL: | F34 F41 |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:aoz:wpaper:126&r= |
| By: | Vladimir I. Danilov; Alexander V. Karzanov |
| Abstract: | We consider a hypergraph (I,C), with possible multiple (hyper)edges and loops, in which the vertices $i\in I$ are interpreted as agents, and the edges $c\in C$ as contracts that can be concluded between agents. The preferences of each agent i concerning the contracts where i takes part are given by use of a choice function $f_i$ possessing the so-called path independent property. In this general setup we introduce the notion of stable network of contracts. The paper contains two main results. The first one is that a general problem on stable systems of contracts for (I,C,f) is reduced to a set of special ones in which preferences of agents are described by use of so-called weak orders, or utility functions. However, for a special case of this sort, the stability may not exist. Trying to overcome this trouble when dealing with such special cases, we introduce a weaker notion of metastability for systems of contracts. Our second result is that a metastable system always exists. |
| Date: | 2022–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2202.13089&r= |
| By: | Takeshi Fukasawa (Graduate School of Economics, The University of Tokyo and Junior Research Fellow, Research Institute for Economics and Business Administration, Kobe University, JAPAN) |
| Abstract: | This study investigates in what cases a firm's dynamic price-setting behavior can be approximated as static under dynamic demand, by developing a dynamic discrete choice model. Under dynamic demand with random utility shock following Gumbel distribution, this study shows that an oligopolistic firm's optimal price-setting behavior is well approximated by the static one with no strategic consideration, when consumers' conditional choice probabilities (CCPs) of choosing the firm's product are small for all consumer types and state variables. If the condition does not hold, the firm's behavior might be far from static. |
| Keywords: | Dynamic demand; Dynamic price-setting behavior; Static approximation; Monopolistic competition; Dynamic discrete choice |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:kob:dpaper:dp2022-19&r= |
| By: | Peter Reinhard Hansen; Chen Tong |
| Abstract: | We introduce a novel pricing kernel with time-varying variance risk aversion that can explain key pricing kernel puzzles. When combined with the Heston-Nandi GARCH model, the framework yields closed-form expressions for the VIX. We also obtain closed-form expressions for option prices by proposing a novel method that extrapolation from the closed-form VIX. We estimate the model with S&P 500 returns and option prices and find a substantial reduction in pricing errors by permitting time-variation in volatility risk aversion. This reduction is seen for both option pricing and VIX pricing and both in-sample and out-of-sample. The variance risk ratio emerges as a fundamental variable in our framework and we show that it is closely related to economic fundamentals and leading measures of sentiment and uncertainty |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.06943&r= |
| By: | Benjamin Avanzi; Hayden Lau; Mogens Steffensen |
| Abstract: | Optimal reinsurance is a perennial problem in insurance. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some important distinctions. In particular, the surplus of an insurance company is routinely approximated by a Brownian motion, as opposed to the geometric Brownian motion used to model assets in finance. Furthermore, exposure to risk is controlled "downwards" via reinsurance, rather than "upwards" via risky investments. This leads to interesting qualitative differences in the optimal solutions. In this paper, using the martingale method, we derive the optimal proportional, non cheap reinsurance control that maximises the quadratic utility of the terminal value of the insurance surplus. We also consider a number of realistic constraints on the terminal value: a strict lower boundary, the probability (Value at Risk) constraint, and the expected shortfall (conditional Value at Risk) constraints under the $\mathbb{P}$ and $\mathbb{Q}$ measures, respectively. Comparison of the optimal strategies with the optimal solutions in finance are of particular interest. Results are illustrated. |
| Date: | 2022–03 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2203.16108&r= |
| By: | Warut Suksompong; Nicholas Teh |
| Abstract: | We consider the problem of fairly allocating indivisible goods to agents with weights representing their entitlements. A natural rule in this setting is the maximum weighted Nash welfare (MWNW) rule, which selects an allocation maximizing the weighted product of the agents' utilities. We show that when agents have binary valuations, a specific version of MWNW is resource- and population-monotone, satisfies group-strategyproofness, and can be implemented in polynomial time. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2204.03803&r= |