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on Utility Models and Prospect Theory |
| By: | Emanuele Borgonovo; Veronica Cappelli; Fabio Maccheroni; Massimo Marinacci |
| Abstract: | The triplet-based risk analysis of Kaplan and Garrick (1981) is the keystone of state-of-the-art probabilistic risk assesment in several applied elds. This paper performs a sharp embedding of the elements of this framework into the one of formal decision theory, which is mainly con- cerned with the methodological and modelling issues of rational decision making. In order to show the applicability of such an embedding, we also explicitly develop it within a nuclear probabilistic risk assessment, as prescribed by the U.S. NRC. The aim of this exercise is twofold: on the one hand, it gives risk analysis a direct access to the rich toolbox that decision theory has developed, in the last decades, in order to deal with complex layers of uncertainty; on the other, it exposes decision theory to the challenges of risk analysis, thus providing it with broader scope and new stimuli. |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:igi:igierp:556&r=all |
| By: | Glötzl, Erhard |
| Abstract: | For more than 100 years economists have tried to describe economics in analogy to physics, more precisely to classical Newtonian mechanics. The development of the Neoclassical General Equilibrium Theory has to be understood as the result of these efforts. But there are many reasons why General Equilibrium Theory is inadequate: 1. No true dynamics. 2. The assumption of the existence of utility functions and the possibility to aggregate them to one “Master” utility function. 3. The impossibility to describe situations as in “Prisoners Dilemma”, where individual optimization does not lead to a collective optimum. This paper aims at overcoming these problems. It illustrates how not only equilibria of economic systems, but also the general dynamics of these systems can be described in close analogy to classical mechanics. To this end, this paper makes the case for an approach based on the concept of constrained dynamics, analyzing the economy from the perspective of “economic forces” and “economic power” based on the concept of physical forces and the reciprocal value of mass. Realizing that accounting identities constitute constraints in the economy, the concept of constrained dynamics, which is part of the standard models of classical mechanics, can be applied to economics. Therefore it is reasonable to denote such models as Newtonian Constraint Dynamic Models (NCD-Models). Such a framework allows understanding both Keynesian and neoclassical models as special cases of NCD-Models in which the power relationships with respect to certain variables are one-sided. As mixed power relationships occur more frequently in reality than purely one-sided power constellations, NCD-models are better suited to describe the economy than standard Keynesian or Neoclassic models. A NCD-model can be understood as “Continuous Time”, “Stock Flow Consistent”, “Agent Based Model”, where the behavior of the agents is described with a general differential equation for every agent. In the special case where the differential equations can be described with utility functions, the behavior of every agent can be understood as an individual optimization strategy. He thus seeks to maximize his utility. However, while the core assumption of neoclassical models is that due to the “invisible hand” such egoistic individual behavior leads to an optimal result for all agents, reality is often defined by “Prisoners Dilemma” situations, in which individual optimization leads to the worst outcome for all. One advantage of NCD-models over standard models is that they are able to describe also such situations, where an individual optimization strategy does not lead to an optimum result for all agents. This will be illustrated in a simple example. In conclusion, the big merit and effort of Newton was, to formalize the right terms (physical force, inertial mass, change of velocity) and to set them into the right relation. Analogously the appropriate terms of economics are force, economic power and change of flow variables. NCD-Models allow formalizing them and setting them into the right relation to each other. |
| Keywords: | Newtonian Constrained Dynamics, Disequilibrium Dynamics, Economics of Power, Closure, Prisoners Dilemma, Economics and Physics |
| JEL: | B22 B41 C02 C60 C72 E10 |
| Date: | 2015–03–29 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:66265&r=all |
| By: | Bernt {\O}ksendal; Elin R{\o}se |
| Abstract: | We present a new approach to the optimal portfolio problem for an insider with logarithmic utility. Our method is based on white noise theory, stochastic forward integrals, Hida-Malliavin calculus and the Donsker delta function. |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1508.06376&r=all |
| By: | Carla Mereu; Robert Stelzer |
| Abstract: | We consider the problem of utility maximization with exponential preferences in a market where the traded stock/risky asset price is modelled as a L\'evy-driven pure jump process (i.e. the driving L\'evy process has no Brownian component). In this setting, we study the terminal utility optimization problem in the presence of a European contingent claim. We consider in detail the BSDE (backward stochastic differential equations) characterising the value function. First we analyse the well-definedness of the generator. This leads to some conditions on the market model related to conditions for the market to admit no free lunches. Then we give bounds on the candidate optimal strategy. Thereafter, we discuss the example of a cross-hedging problem and, under severe assumptions on the structure of the claim, we give explicit solutions. Finally, we establish an explicit solution for a related BSDE with a suitable terminal condition but a simpler generator. |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1508.07561&r=all |
| By: | Antonin Pottier (CERNA - Centre d'économie industrielle - MINES ParisTech - École nationale supérieure des mines de Paris) |
| Abstract: | Dietz and Matei (2015) introduce Time-Stochastic Dominance and apply it to evaluate climate-change mitigation. They compute several preferences classes for which mitigation policies are preferred to business-as-usual. The purpose of the present study is to investigate which standard utility functions (with constant time-discount rate and a constant risk aversion) belong to them. The major contribution is to map preferences classes studied by Dietz and Matei (2015) into the space of time-discount rate and elasticity of marginal utility of consumption, space in which the climate debate has been shaped so far. |
| Date: | 2015–01–29 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01185848&r=all |
| By: | L. A. Bordag (University of Applied Sciences Zittau/Goerlitz, Zittau, Germany); I. P. Yamshchikov (University of Applied Sciences Zittau/Goerlitz, Zittau, Germany); D. Zhelezov (Mathematical Sciences, University of Gothenburg, Gothenburg, Sweden) |
| Abstract: | Management of the portfolios containing low liquidity assets is a tedious problem. The buyer proposes the price that can differ greatly from the paper value estimated by the seller, so the seller can not liquidate his portfolio instantly and waits for a more favorable offer. To minimize losses and move the theory towards practical needs one can take into account the time lag of the liquidation of an illiquid asset. Working in the Merton's optimal consumption framework with continuous time we consider an optimization problem for a portfolio with an illiquid, a risky and a risk-free asset. While a standard Black-Scholes market describes the liquid part of the investment the illiquid asset is sold at an exogenous random moment with prescribed liquidation time distribution. The investor has the logarithmic utility function as a limit case of a HARA-type utility. Different distributions of the liquidation time of the illiquid asset are under consideration-a classical exponential distribution and Weibull distribution that is more practically relevant. Under certain conditions we show the existence of the viscosity solution in both cases. Applying numerical methods we compare classical Merton's strategies and the optimal consumption-allocation strategies for portfolios with different liquidation time distributions of an illiquid asset. KEYWORDS portfolio optimization — illiquidity — viscosity solutions — random income |
| Date: | 2015–04–30 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-01186961&r=all |
| By: | Lin Zhao (University of Amsterdam, the Netherlands); Sweder van Wijnbergen (University of Amsterdam, the Netherlands) |
| Abstract: | We investigate the relationship between the gas spot market and the price of gas storage capacity. Contrary to the common belief, the auction prices for gas storage are mostly affected by the volatility of current market prices rather than by the winter-summer price differences. This paper provides a numerical solution for pricing storage capacity, by taking investor's activities through the spot market and storage service into account. A bivariate Generalized Autoregressive Score (GAS) model is employed for modeling the dynamics of the day-ahead and month-ahead spot market prices, as well as the time-varying volatilities and correlations. Under an incomplete market setting, our model is able to approximate the realized auction prices. Moreover, one interesting implication is that the implied average risk aversion of investor for a storage contract increases with the volatility of the spot market. This is an intuitive result because storage capacity can serve as an effective hedging product for the spot market, and the demand for this product is high when the market becomes risky: more risk averse investors are participating in the auctions. Moreover, a sensitivity analysis on different injection/withdrawal rates is also included, and particularly, contracts with higher capacity rates are priced at a higher level. |
| Keywords: | stochastic volatility; Generalised Autoregressive Score modeling; incomplete markets; real options; utility indifference pricing; gas storage; capacity constraints |
| JEL: | C61 C63 G12 G13 Q41 |
| Date: | 2015–08–28 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150104&r=all |
| By: | Acharya, Avidit (Stanford University); Blackwell, Matthew (Harvard University); Sen, Maya (Harvard University) |
| Abstract: | The standard approach in positive political theory posits that action choices are the consequences of attitudes. Could it be, however, that an individual's actions also affect her fundamental preferences? We present a broad theoretical framework that captures the simple, yet powerful, intuition that actions frequently alter attitudes as individuals seek to minimize cognitive dissonance. This framework is particularly appropriate for the study of political attitudes and enables political scientists to formally address questions that have remained inadequately answered by conventional rational choice approaches--questions such as "What are the origins of partisanship?" and "What drives ethnic and racial hatred?" We illustrate our ideas with three examples from the literature: (1) how partisanship emerges naturally in a two party system despite policy being multidimensional, (2) how ethnic or racial hostility increases after acts of violence, and (3) how interactions with people who express different views can lead to empathetic changes in political positions. |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:harjfk:rwp15-026&r=all |
| By: | Wendy Janssens (VU University Amsterdam, the Netherlands.); Berber Kramer (International Food Policy Research Institute (IFPRI), United States); Lisette Swart (VU University Amsterdam,the Netherlands) |
| Abstract: | Most evidence of hyperbolic discounting is based on violations of either stationarity or time consistency as observed in choice experiments. These choice reversals may however also result from time-varying discount rates. Hyperbolic discounting is a plausible explanation for choice reversals only if violations of stationarity and time consistency overlap. Our field experiment examines the extent to which this is the case. At different points in time, the same participants allocated a future gift over sooner-smaller and later-larger rewards with varying front-end delays. We find that most violations of time consistency do not coincide with violations of stationarity. This is surprisingly similar to what an earlier experiment on stationarity, time invariance and time consistency finds using a different design among a different type of participants (Halevy, Econometrica , 2015). Random noise in decision-making alone does not explain this finding, given that we find a significant association between changes in household wealth and violations of stationarity and time consistency. We conclude that when incomes fluctuate, one can only identify hyperbolic discounting by eliciting violations of both stationarity and time consistency through a longitudinal design for the same subject pool. |
| Keywords: | Time preferences; present bias; temporal stability |
| JEL: | C93 D03 D14 D90 G02 |
| Date: | 2015–08–14 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150097&r=all |
| By: | Walter Hyll; Maike Irrek |
| Abstract: | Several scholars analyze the relationship between individuals’ willingness to take risks and financial investment decisions. We add to this literature in using data from the German Socio-Economic Panel which allow ruling out that investments in risky assets itself impact on risk attitudes. We show that individuals with a higher willingness to take risks are more likely to hold bonds, stocks, and company assets. When grouping individuals into risk groups, our results reveal that high risk takers are also less likely to own a life insurance. If endogenous adaption of risk attitudes from holding assets in previous years is not taken into account, the impact of risk attitudes on holding risky assets is upward biased. |
| Keywords: | risk attitudes, financial investment, portfolio choice, reverse causality, German Socio-Economic Panel |
| JEL: | D14 D81 G11 |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:iwh:dispap:10-15&r=all |
| By: | Noé Biheng (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics); Jean-Marc Bonnisseau (EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS) |
| Abstract: | We consider a family of exchange economies with complete markets where consumers have multiprior preferences representing their ambiguity aversion. Under a linear independence assumption, we prove that regular economies are generic. Regular economies exhibit enjoyable properties: odd finite number of equilibrium prices, local constancy of this number, local differentiable selections of the equilibrium prices. Thus, even if ambiguity aversion is represented by non-differentiable multiprior preferences, economies retain generically the properties of the differentiable approach. |
| Date: | 2015 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01185486&r=all |
| By: | Hao Xing |
| Abstract: | This paper studies stability of the exponential utility maximization when there are small variations on agent's utility function. Two settings are considered. First, in a general semi-martingale model where random endowments are present, a sequence of utilities depned on R converges to the exponential utility. Under a uniform condition on their marginal utilities, convergence of value functions, optimal payouts and optimal investment strategies are obtained, their rate of con-vergence are also determined. Stability of utility-based pricing is studied as an application. Second, a sequence of utilities depened on R+ converges to the exponential utility after shifting and scaling. Their associated optimal strategies, after appropriate scaling, converge to the optimal strategy for the exponential hedging problem. This complements Theorem 3.2 in M. Nutz, Probab. Theory Relat. Fields, 152, 2012, which establishes the convergence for a sequence of power utilities. |
| JEL: | C1 F3 G3 |
| Date: | 2014–03–24 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:57213&r=all |
| By: | Miklos Rasonyi |
| Abstract: | We treat an infinite dimensional optimization problem arising in economic theory. Under appropriate conditions, we show the existence of an optimal strategy for an investor trading in the classical Arbitrage Pricing Model of S. A. Ross. As a consequence, we derive the existence of equivalent risk-neutral measures of a particular form which have favourable integrability properties. |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1508.07761&r=all |
| By: | Francesco Bogliacino; Pietro Ortoleva |
| Abstract: | We use prospect theory to model reference dependent consumers, where the reference point is the average behavior of the society in the current period. We show that after a finite number of steps under any equilibrium, the distribution of wealth will become and remain equal, or admit a missing class (a particular form of polarization). Under equilibria that admit the highest growth rates, the initial wealth distribution that maximizes this growth rate is one of perfect equality. Conversely, under equilibria that admit the lowest growth rates, perfect equality minimizes this growth rate and societies with a small level of initial inequality grow the fastest. In addition growth rates in corresponding economics without reference dependent consumers admit lower growth rates. |
| Keywords: | Prospect Theory, Reference-dependence, Aspirations |
| JEL: | D11 D91 |
| Date: | 2015–08–25 |
| URL: | http://d.repec.org/n?u=RePEc:col:000178:013611&r=all |