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on Utility Models and Prospect Theory |
| By: | Eric Danan (THEMA - Théorie économique, modélisation et applications - CNRS : UMR8184 - Université de Cergy Pontoise); Thibault Gajdos (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - École des Hautes Études en Sciences Sociales (EHESS) - CNRS : UMR7316); Jean-Marc Tallon (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris 1 - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris) |
| Abstract: | We provide a generalization of Harsanyi (1955)'s aggregation theorem to the case of incomplete preferences at the individual and social level. Individuals and society have possibly incomplete expected utility preferences that are represented by sets of expected utility functions. Under Pareto indifference, social preferences are represented through a set of aggregation rules that are utilitarian in a generalized sense. Strengthening Pareto indifference to Pareto preference provides a refinement of the representation. |
| Keywords: | Incomplete preferences; aggregation; expected multi-utility; utilitarianism |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00941799&r=upt |
| By: | R.A Dana; Cuong Le Van |
| Abstract: | This article reconsiders the theory of existence of efficient allocations and equilibria when consumption sets are unbounded below under the assumption that agents have incomplete preferences. It is motivated by an example in the theory of assets with short-selling where there is risk and ambiguity. Agents have Bewley’s incomplete preferences. As an inertia principle is assumed in markets, equilibria are individually rational. It is shown that a necessary and sufficient for existence of an individually rational efficient allocation or of an equilibrium is that the relative interiors of the risk adjusted sets of probabilities intersect. The more risk averse, the more ambiguity averse the agents, the more likely is an equilibrium to exist. The paper then turns to incomplete preferences with concave multi-utility representations. Several definitions of efficiency and of equilibrium with inertia are considered. Sufficient conditions and necessary and sufficient conditions are given for existence of efficient allocations and equilibria with inertia. |
| Keywords: | Uncertainty, risk, risk adjusted prior, no arbitrage, equilibrium with short-selling, incomplete preferences, equilibrium with inertia. |
| JEL: | C62 D50 D81 D84 G1 |
| Date: | 2014–01–06 |
| URL: | http://d.repec.org/n?u=RePEc:ipg:wpaper:2014-061&r=upt |
| By: | Bin Zou; Abel Cadenillas |
| Abstract: | Motivated by the AIG bailout case in the financial crisis of 2007-2008, we consider an insurer who wants to maximize the expected utility of the terminal wealth by selecting optimal investment and risk control strategies. The insurer's risk process is modelled by a jump-diffusion process and is negatively correlated with the capital gains in the financial market. We obtain explicit solution to optimal strategies for various utility functions. |
| Date: | 2014–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1402.3560&r=upt |
| By: | Oumar Mbodji (Department of Mathematics and Statistics [Hamilton] - McMaster University); Adrien Nguyen Huu (FiME Lab - Laboratoire de Finance des Marchés d'Energie - Université Paris IX - Paris Dauphine - CREST - EDF R&D, IMPA - Instituto Nacional de Matemática Pura e Aplicada - Instituto Nacional de matematica pura e aplicada); Traian A. Pirvu (Department of Mathematics and Statistics - McMaster University) |
| Abstract: | We study the Merton problem of optimal consumption-investment for the case of two investors sharing a final wealth. The typical example would be a husband and wife sharing a portfolio looking to optimize the expected utility of consumption and final wealth. Each agent has different utility function and discount factor. An explicit formulation for the optimal consumptions and portfolio can be obtained in the case of a complete market. The problem is shown to be equivalent to maximizing three different utilities separately with separate initial wealths. We study a numerical example where the market price of risk is assumed to be mean reverting, and provide insights on the influence of risk aversion or discount rates on the initial optimal allocation. |
| Keywords: | portfolio optimization; time inconsistency; portfolio management; optimal consumption; market price of risk |
| Date: | 2014–01–31 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00940233&r=upt |
| By: | G. Carlier; R.-A. Dana |
| Abstract: | An exchange economy in which agents have convex incomplete preferences defined by families of concave utility functions is consid- ered. Sufficient conditions for the set of efficient allocations and equi- libria to coincide with the set of efficient allocations and equilibria that result when each agent has a utility in her family are provided. Welfare theorems in an incomplete preferences framework therefore hold under these conditions and efficient allocations and equilibria are characterized by first order conditions. |
| Keywords: | incomplete preferences, efficient allocations and equilibria. |
| Date: | 2014–01–06 |
| URL: | http://d.repec.org/n?u=RePEc:ipg:wpaper:2014-060&r=upt |
| By: | Bin Zou; Abel Cadenillas |
| Abstract: | We generalize Merton's framework by incorporating an insurable loss. Motivated by new insurance products, we allow not only the financial market but also the insurable loss to depend on the regime of the economy. An investor wants to select an optimal consumption, investment, and insurance policy that maximizes his expected total discounted utility of consumption over an infinite time horizon. For the case of hyperbolic absolute risk aversion (HARA) utility functions, we obtain the first explicit solutions for optimal consumption, investment, and insurance problem when there is regime switching. We determine that the optimal insurance contract is either no-insurance or deductible insurance, and calculate when it is optimal to buy insurance. The optimal policy depends strongly on the regime of the economy. Through an economic analysis, we calculate the advantage of buying insurance. We also observe that as long as optimal insurance is nonzero in one regime, investors gain benefits in all regimes from insurance. |
| Date: | 2014–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1402.3562&r=upt |
| By: | H. Youn Kim; Keith R. McLaren; K.K. Gary Wong |
| Abstract: | This paper integrates seemingly disjoint studies on consumer behavior in micro and macro analyses via the intertemporal two-stage budgeting procedure with durable goods and liquidity constraints. The model accounts for the influences of nondurables consumption, commodity prices, and durables stock on commodity demands as well as on risk aversion and asset returns. The demand functions for six nondurable goods are jointly estimated with the Euler equations for bonds, shares, and durables goods, with allowance for liquidity constraints. The integrated model proves useful with new findings for risk aversion and, particularly, an extended consumption CAPM with multiple goods and liquidity constraints. |
| Keywords: | Intertemporal two-stage budgeting; Indirect utility function; Risk aversion; The stochastic discount factor; Consumption-based CAPM |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2014-4&r=upt |
| By: | Keith R. McLaren; Ou Yang |
| Abstract: | A class of demand systems based on simple parametric specification of the indirect utility functions, but allowing for the parsimonious imposition of global regularity, is proposed. Demand systems in this class are completely flexible in rank, i.e., can be potentially specified to acquire as large a rank as required in empirical work. They also exhibit a clear and reasonable homothetic asymptotic behaviour. In an empirical application using Australian data, several examples from this class are estimated and compared with some popular alternatives in the literature. |
| Keywords: | Demand systems; Global regularity; Complete rank flexibility; Duality theory; Indirect utility function |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2014-6&r=upt |
| By: | Andersson, Henrik (Toulouse School of Economics); Risa Hole, Arne (University of Sheffield); Svensson, Mikael (Dept. of Economics) |
| Abstract: | This study elicits individual preferences for reducing morbidity and mortality risk in the context of an infectious disease (campylobacter) using choice experiments. Respondents are in the survey asked to choose between different policies that, in addition to the two health risks, also vary with respect to source of disease being targeted (food or water), when the policy takes place (in time), and the monetary cost. Our results in our baseline model are in line with expectations; respondents prefer the benefits of the program sooner than later, programs that reduce both the mortality and morbidity risk, and less costly programs. Moreover, our results suggest that respondents prefer water- compared with food-safety programs. However, a main objective of this study is to examine scope sensitivity of mortality risk reductions using a novel approach. Our results from a split-sample design suggest that the value of the mortality risk reduction, defined as the value of a statistical life, is SEK 3 177 (USD 483 million) and SEK 50 million (USD 8 million), respectively, in our two sub-samples. This result cast doubt on the standard scope sensitivity tests in choice experiments, and the results also cast doubt on the validity and reliability of VSL estimates based on stated preference (and revealed preference) studies in general. This is important due to the large empirical literature on non-market evaluation and the elicited values’ central role in policy making, such as benefit-cost analysis. |
| Keywords: | Choice experiments; Morbidity risk; Mortality risk; Scope sensitivity; Willingness to pay |
| JEL: | D61 H41 I18 Q51 |
| Date: | 2014–02–06 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:kaunek:0011&r=upt |