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on Utility Models and Prospect Theory |
| By: | Jocelyne Bion-Nadal; Magali Kervarec |
| Abstract: | The framework of this paper is that of uncertainty, that is when no reference probability measure is given. To every convex regular risk measure $\rho$ on ${\cal C}_b(\Omega)$, we associate a canonical $c_{\rho}$-class of probability measures. Furthermore the convex risk measure admits a dual representation in terms of a weakly relatively compact set of probability measures absolutely continuous with respect to some probability measure belonging to the canonical $c_{\rho}$-class. To get these results we study the topological properties of the dual of the Banach space $L^1(c)$ associated to some capacity $c$ and we prove a representation Theorem for convex risk measures on $L^1(c)$. As applications, we obtain that every $G$-expectation $\E$ (resp. in case of uncertain volatility every sublinear risk measure $\rho$), admits a representation with a numerable family of probability measures absolutely continuous with respect to some $P$ belonging to the canonical $c$-class, with $c(f)=\E(|f|)$, (resp. $\rho(-|f|))$. |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1004.5524&r=upt |
| By: | Benchimol, Jonathan (CES, University Paris 1 Panthéon-Sorbonne and Department of Economics, ESSEC Business School); Fourçans, André (ESSEC Business School, Department of Economics) |
| Abstract: | In this paper, we set up and test a model of the Euro zone, with a special emphasis on the role of money. The model follows the New Keynesian DSGE framework, money being introduced in the utility function with a non-separability assumption. By using bayesian estimation techniques, we shed light on the determinants of output and inflation, but also of the interest rate, real money balances, flexible-price output and flexible-price real money balances variances. The role of money is investigated further. We find that its impact on output depends on the degree of agents’ risk aversion, increases with this degree, and becomes significant when risk aversion is high enough. The direct impact of the money variable on inflation variability is essentially minor whatever the risk aversion level, the interest rate (monetary policy) being the overwhelming explanatory factor. |
| Keywords: | Bayesian Estimation; DSGE Model; Euro Area; Money |
| JEL: | E31 E51 E58 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:ebg:essewp:dr-10005&r=upt |
| By: | Nicole El Karoui (CMAP - Centre de Mathématiques Appliquées - CNRS : UMR7641 - Polytechnique - X, PMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Pierre et Marie Curie - Paris VI - Université Paris-Diderot - Paris VII); Mohamed M'Rad (CMAP - Centre de Mathématiques Appliquées - CNRS : UMR7641 - Polytechnique - X) |
| Abstract: | The paper proposes a new approach to consistent stochastic utilities, also called forward dynamic utility, recently introduced by M. Musiela and T. Zariphopoulou. These utilities satisfy a property of consistency with a given incomplete financial market which gives them properties similar to the function values of classical portfolio optimization. First, we derive a non linear stochastic PDEs that satisfy consistent stochastic utilities processes of Itô type and their dual convex conjugates. Then, under some assumptions of regularity and monotony on the stochastic flow associated with the optimal wealth as function of the initial capital, and on the optimal state price dual process, we characterize all consistent utilities for a given increasing optimal wealth process from the composition of the dual optimal process and the inverse of the optimal wealth. This allows us to reduce the resolution of fully nonlinear second order utility SPDE to the existence of monotone solutions of two stochastic differential equations. We also, express the volatility of consistent utilities as an operator of the first and the second order derivatives of the utility in terms of the optimal primal and dual policies. |
| Keywords: | forward utility; performance criteria; horizon-unbiased utility; consistent utility; progressive utility; portfolio optimization; optimal portfolio; duality; minimal martingale measure; Stochastic flows SDE; Stochastic partial differential equations; |
| Date: | 2010–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00477381_v1&r=upt |
| By: | Ron Bird (School of Finance and Economics, University of Technology, Sydney); Danny Yeung (School of Finance and Economics, University of Technology, Sydney) |
| Abstract: | It has long been accepted in finance that risk plays an important role in determining valuation where risk reflects that investors are unsure as to the exact value of future returns but are able to express their prior expectations by way of a probability distribution of these returns. Knights (1921) introduced the concept of uncertainty where we possess incomplete knowledge about this distribution and so are unable to formulate priors over all possible outcomes. A number of writers (Gilboa and Schmeidler, 1989; Epstein and Schneider, 2003) have developed models that suggest that ambiguity, like risk, has a negative impact on valuation. The most common approach taken in these models is to assume that investors take a conservative approach when faced with uncertainty and base their decisions on the worst case scenario (maxmin expected utility). The area on which we concentrate in this paper is how the market faced with uncertainty reacts to the receipt of new information. The proposition being that under maxmin expected utility, the interpretation that the market will place on any information received will become more pessimistic as uncertainty increases, upgrading any bad news and downgrading any good news. Williams (2009) uses changes in the VIX (i.e. implied market volatility) as a measure of market uncertainty in his US study where he evaluates the markets response to the release of earnings news. There is a plethora of evidence dating back to Ball and Brown (1968) that confirms that the market responds positively (negatively) to good (bad) news earnings announcements. Williams finds that this response is conditioned by market uncertainty with there being the predicted asymmetric reaction to good and bad earnings news – the negative reaction to bad news increasing with uncertainty and the positive reaction to good news decreasing. In this study we use Australian data to also examine the impact of uncertainty on the market response to earnings announcements. One important difference in our findings to those of Williams is that it is not only changes in VIX but also the level of VIX that influence how the market responds to earnings information. Although generally confirming a pessimistic response by investors to earnings released at a time of high market uncertainly, we find evidence of a slight optimistic bias in the reaction of investors to earnings released at a time of low market uncertainty. We also find that the level of pessimism engendered when uncertainly is high may be significantly diluted if it occurs contemporaneously with strong market sentiment. |
| Date: | 2010–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:uts:pwcwps:8&r=upt |
| By: | N. El Karoui (CMAP - Centre de Mathématiques Appliquées - CNRS : UMR7641 - Polytechnique - X, PMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Pierre et Marie Curie - Paris VI - Université Paris-Diderot - Paris VII); Mohamed M'Rad (CMAP - Centre de Mathématiques Appliquées - CNRS : UMR7641 - Polytechnique - X) |
| Abstract: | The paper generalizes the construction by stochastic flows of consistent utilities processes introduced by M. Mrad and N. El Karoui (2010). The market is incomplete and securities are modeled as locally bounded positive semimartingales. Making minimal assumptions and convex constraints on test-portfolios, we construct by composing two stochastic flows of homeomorphisms, all the consistent stochastic utilities whose the optimal wealth process is a given admissible portfolio, strictly increasing in initial capital. Proofs are essentially based on change of variables techniques. |
| Keywords: | Consistent utilities; progressive utilities;forward utility, performance criteria, horizon-unbiased utility, consistent utility; progressive utility; portfolio optimization; optimal portfolio; duality;minimal martingal measure;Stochastic flows of homeomorphisms |
| Date: | 2010–04–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00477380_v1&r=upt |
| By: | Claudia Miani (Bank of Italy); Stefano Siviero (Bank of Italy) |
| Abstract: | It has increasingly become standard practice to supplement point macroeconomic forecasts with an appraisal of the degree of uncertainty and the prevailing direction of risks. Several alternative approaches have been proposed in the literature to compute the probability distribution of macroeconomic forecasts; all of them rely on combining the predictive density of model-based forecasts with subjective judgment about the direction and intensity of prevailing risks. We propose a non-parametric, model-based simulation approach, which does not require specific assumptions to be made regarding the probability distribution of the sources of risk. The probability distribution of macroeconomic forecasts is computed as the result of model-based stochastic simulations which rely on re-sampling from the historical distribution of risk factors and are designed to deliver the desired degree of skewness. By contrast, other approaches typically make a specific, parametric assumption about the distribution of risk factors. The approach is illustrated using the Bank of Italy’s Quarterly Macroeconometric Model. The results suggest that the distribution of macroeconomic forecasts quickly tends to become symmetric, even if all risk factors are assumed to be asymmetrically distributed. |
| Keywords: | macroeconomic forecasts, stochastic simulations, balance of risks, uncertainty, fan-charts |
| JEL: | C14 C53 E37 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:bdi:wptemi:td_758_10&r=upt |
| By: | Giuseppe Cappelletti (Bank of Italy) |
| Abstract: | Rationalizability is a widely accepted solution concept in the study of strategic form game with complete information and is fully characterized in terms of assumptions on the rationality of the players and common certainty of rationality. Battigalli and Siniscalchi extend rationalizability and derive the solution concept called Δ-rationalizability. Their analysis is based on the following assumptions: (a) players are rational; (b) their first-order beliefs satisfy some restrictions; and (c) there is common belief of (a) and (b). In this note I focus on games with complete information and I characterize Δ-rationalizability with a new notion of iterative dominance which is able to capture the additional hypothesis on players' beliefs. |
| Keywords: | rationalizability, strategic form game, complete information |
| JEL: | C72 |
| Date: | 2010–04 |
| URL: | http://d.repec.org/n?u=RePEc:bdi:wptemi:td_757_10&r=upt |