Risk sensitivity in a motor task with speed-accuracy trade-off.

When a racing driver steers a car around a sharp bend, there is a trade-off between speed and accuracy, in that high speed can lead to a skid whereas a low speed increases lap time, both of which can adversely affect the driver's payoff function. While speed-accuracy trade-offs have been studied extensively, their susceptibility to risk sensitivity is much less understood, since most theories of motor control are risk neutral with respect to payoff, i.e., they only consider mean payoffs and ignore payoff variability. Here we investigate how individual risk attitudes impact a motor task that involves such a speed-accuracy trade-off. We designed an experiment where a target had to be hit and the reward (given in points) increased as a function of both subjects' endpoint accuracy and endpoint velocity. As faster movements lead to poorer endpoint accuracy, the variance of the reward increased for higher velocities. We tested subjects on two reward conditions that had the same mean reward but differed in the variance of the reward. A risk-neutral account predicts that subjects should only maximize the mean reward and hence perform identically in the two conditions. In contrast, we found that some (risk-averse) subjects chose to move with lower velocities and other (risk-seeking) subjects with higher velocities in the condition with higher reward variance (risk). This behavior is suboptimal with regard to maximizing the mean number of points but is in accordance with a risk-sensitive account of movement selection. Our study suggests that individual risk sensitivity is an important factor in motor tasks with speed-accuracy trade-offs.

Risk-sensitive optimal feedback control accounts for sensorimotor behavior under uncertainty

Many aspects of human motor behavior can be understood using optimality principles such as optimal feedback control. However, these proposed optimal control models are risk-neutral; that is, they are indifferent to the variability of the movement cost. Here, we propose the use of a risk-sensitive optimal controller that incorporates movement cost variance either as an added cost (risk-averse controller) or as an added value (risk-seeking controller) to model human motor behavior in the face of uncertainty. We use a sensorimotor task to test the hypothesis that subjects are risk-sensitive. Subjects controlled a virtual ball undergoing Brownian motion towards a target. Subjects were required to minimize an explicit cost, in points, that was a combination of the final positional error of the ball and the integrated control cost. By testing subjects on different levels of Brownian motion noise and relative weighting of the position and control cost, we could distinguish between risk-sensitive and risk-neutral control. We show that subjects change their movement strategy pessimistically in the face of increased uncertainty in accord with the predictions of a risk-averse optimal controller. Our results suggest that risk-sensitivity is a fundamental attribute that needs to be incorporated into optimal feedback control models. © 2010 Nagengast et al.

The Effect of Risk Sensitivity on Collaborative New Product Development in a Supply Chain

The increasing risks and costs of new product development require firms to collaborate with their supply chain partners in product management. In this paper, a supply chain model is proposed with one risk-neutral supplier and one risk-averse manufacturer. The manufacturer has an opportunity to enhance demand by developing a new product, but both the actual demand for new product and the supplier’s wholesale price are uncertain. The supplier has an incentive to share risks of new product development via an advance commitment to wholesale price for its own profit maximization. The effects of the manufacturer’s risk sensitivity on the players’ optimal strategies are analyzed and the trade-off between innovation incentives and pricing flexibility is investigated from the perspective of the supplier. The results highlight the significant role of risk sensitivity in collaborative new product development, and it is found that the manufacturer’s innovation level and retail price are always decreasing in the risk sensitivity, and the supplier prefers commitment to wholesale price only when the risk sensitivity is below a certain threshold.

Trading the differences in expectations between the CDS and bond markets

This paper uses the framework developed by Vrugt (2010) to extract the recovery rate and term-structure of risk-neutral default probabilities implied in the cross-section of Portuguese sovereign bonds outstanding between March and August 2011. During this period the expectations on the recovery rate remain firmly anchored around 50 percent while the instantaneous default probability increases steadily from 6 to above 30 percent. These parameters are then used to calculate the fair-value of a 5-year and 10- year CDS contract. A credit-risk-neutral strategy is developed from the difference between the market price of a CDS of the same tenors and the fair-value calculated, yielding a sharpe ratio of 3.2

A Survey Measure of Risk Aversion

We Use Survey Data on the Well-Being of Individuals to Measure Attitude Toward Risk. Risk Neutrality Cannot Be Rejected by the Data.

Modélisation du carnet d'ordres limites et prévision de séries temporelles

Le contenu de cette thèse est divisé de la façon suivante. Après un premier chapitre d’introduction, le Chapitre 2 est consacré à introduire aussi simplement que possible certaines des théories qui seront utilisées dans les deux premiers articles. Dans un premier temps, nous discuterons des points importants pour la construction de l’intégrale stochastique par rapport aux semimartingales avec paramètre spatial. Ensuite, nous décrirons les principaux résultats de la théorie de l’évaluation en monde neutre au risque et, finalement, nous donnerons une brève description d’une méthode d’optimisation connue sous le nom de dualité. Les Chapitres 3 et 4 traitent de la modélisation de l’illiquidité et font l’objet de deux articles. Le premier propose un modèle en temps continu pour la structure et le comportement du carnet d’ordres limites. Le comportement du portefeuille d’un investisseur utilisant des ordres de marché est déduit et des conditions permettant d’éliminer les possibilités d’arbitrages sont données. Grâce à la formule d’Itô généralisée il est aussi possible d’écrire la valeur du portefeuille comme une équation différentielle stochastique. Un exemple complet de modèle de marché est présenté de même qu’une méthode de calibrage. Dans le deuxième article, écrit en collaboration avec Bruno Rémillard, nous proposons un modèle similaire mais cette fois-ci en temps discret. La question de tarification des produits dérivés est étudiée et des solutions pour le prix des options européennes de vente et d’achat sont données sous forme explicite. Des conditions spécifiques à ce modèle qui permettent d’éliminer l’arbitrage sont aussi données. Grâce à la méthode duale, nous montrons qu’il est aussi possible d’écrire le prix des options européennes comme un problème d’optimisation d’une espérance sur en ensemble de mesures de probabilité. Le Chapitre 5 contient le troisième article de la thèse et porte sur un sujet différent. Dans cet article, aussi écrit en collaboration avec Bruno Rémillard, nous proposons une méthode de prévision des séries temporelles basée sur les copules multivariées. Afin de mieux comprendre le gain en performance que donne cette méthode, nous étudions à l’aide d’expériences numériques l’effet de la force et la structure de dépendance sur les prévisions. Puisque les copules permettent d’isoler la structure de dépendance et les distributions marginales, nous étudions l’impact de différentes distributions marginales sur la performance des prévisions. Finalement, nous étudions aussi l’effet des erreurs d’estimation sur la performance des prévisions. Dans tous les cas, nous comparons la performance des prévisions en utilisant des prévisions provenant d’une série bivariée et d’une série univariée, ce qui permet d’illustrer l’avantage de cette méthode. Dans un intérêt plus pratique, nous présentons une application complète sur des données financières.

Risk Aversion in Inventory Management

Traditional inventory models focus on risk-neutral decision makers, i.e., characterizing replenishment strategies that maximize expected total profit, or equivalently, minimize expected total cost over a planning horizon. In this paper, we propose a framework for incorporating risk aversion in multi-period inventory models as well as multi-period models that coordinate inventory and pricing strategies. In each case, we characterize the optimal policy for various measures of risk that have been commonly used in the finance literature. In particular, we show that the structure of the optimal policy for a decision maker with exponential utility functions is almost identical to the structure of the optimal risk-neutral inventory (and pricing) policies. Computational results demonstrate the importance of this approach not only to risk-averse decision makers, but also to risk-neutral decision makers with limited information on the demand distribution.

Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.

The lottery-panel task for bi-dimensional parameter-free elicitation of risk attitudes

We propose first, a simple task for the eliciting attitudes toward risky choice, the SGG lottery-panel task, which consists in a series of lotteries constructed to compensate riskier options with higher risk-return trade-offs. Using Principal Component Analysis technique, we show that the SGG lottery-panel task is capable of capturing two dimensions of individual risky decision making i.e. subjects’ average risk taking and their sensitivity towards variations in risk-return. From the results of a large experimental dataset, we confirm that the task systematically captures a number of regularities such as: A tendency to risk averse behavior (only around 10% of choices are compatible with risk neutrality); An attraction to certain payoffs compared to low risk lotteries, compatible with over-(under-) weighting of small (large) probabilities predicted in PT and; Gender differences, i.e. males being consistently less risk averse than females but both genders being similarly responsive to the increases in risk-premium. Another interesting result is that in hypothetical choices most individuals increase their risk taking responding to the increase in return to risk, as predicted by PT, while across panels with real rewards we see even more changes, but opposite to the expected pattern of riskier choices for higher risk-returns. Therefore, we conclude from our data that an “economic anomaly” emerges in the real reward choices opposite to the hypothetical choices. These findings are in line with Camerer's (1995) view that although in many domains, paid subjects probably do exert extra mental effort which improves their performance, choice over money gambles is not likely to be a domain in which effort will improve adherence to rational axioms (p. 635). Finally, we demonstrate that both dimensions of risk attitudes, average risk taking and sensitivity towards variations in the return to risk, are desirable not only to describe behavior under risk but also to explain behavior in other contexts, as illustrated by an example. In the second study, we propose three additional treatments intended to elicit risk attitudes under high stakes and mixed outcome (gains and losses) lotteries. Using a dataset obtained from a hypothetical implementation of the tasks we show that the new treatments are able to capture both dimensions of risk attitudes. This new dataset allows us to describe several regularities, both at the aggregate and within-subjects level. We find that in every treatment over 70% of choices show some degree of risk aversion and only between 0.6% and 15.3% of individuals are consistently risk neutral within the same treatment. We also confirm the existence of gender differences in the degree of risk taking, that is, in all treatments females prefer safer lotteries compared to males. Regarding our second dimension of risk attitudes we observe, in all treatments, an increase in risk taking in response to risk premium increases. Treatment comparisons reveal other regularities, such as a lower degree of risk taking in large stake treatments compared to low stake treatments and a lower degree of risk taking when losses are incorporated into the large stake lotteries. Results that are compatible with previous findings in the literature, for stake size effects (e.g., Binswanger, 1980; Antoni Bosch-Domènech & Silvestre, 1999; Hogarth & Einhorn, 1990; Holt & Laury, 2002; Kachelmeier & Shehata, 1992; Kühberger et al., 1999; B. J. Weber & Chapman, 2005; Wik et al., 2007) and domain effect (e.g., Brooks and Zank, 2005, Schoemaker, 1990, Wik et al., 2007). Whereas for small stake treatments, we find that the effect of incorporating losses into the outcomes is not so clear. At the aggregate level an increase in risk taking is observed, but also more dispersion in the choices, whilst at the within-subjects level the effect weakens. Finally, regarding responses to risk premium, we find that compared to only gains treatments sensitivity is lower in the mixed lotteries treatments (SL and LL). In general sensitivity to risk-return is more affected by the domain than the stake size. After having described the properties of risk attitudes as captured by the SGG risk elicitation task and its three new versions, it is important to recall that the danger of using unidimensional descriptions of risk attitudes goes beyond the incompatibility with modern economic theories like PT, CPT etc., all of which call for tests with multiple degrees of freedom. Being faithful to this recommendation, the contribution of this essay is an empirically and endogenously determined bi-dimensional specification of risk attitudes, useful to describe behavior under uncertainty and to explain behavior in other contexts. Hopefully, this will contribute to create large datasets containing a multidimensional description of individual risk attitudes, while at the same time allowing for a robust context, compatible with present and even future more complex descriptions of human attitudes towards risk.

Does liquidity constraints matter for Ricardian equivalence?

The paper analysis a general equilibrium model with two periods, several households and a government that has to finance some expenditures in the first period. Households may have some private information either about their type (adverse selection) or about some action levei chosen in the first period that affects the probability of certain states of nature in the second period (moral hazard). Trade of financiai assets are intermediated by a finite collection of banks. Banks objective functions are determined in equilibrium by shareholders. Due to private information it may be optimal for the banks to introduce constraints in the set of available portfolios for each household as wellas household specific asset prices. In particular, households may face distinct interest rates for holding the risk-free asset. The government finances its expenditures either by taxing households in the first period or by issuing bonds in the first period and taxing households in the second period. Taxes may be state-dependent. Suppose government policies are neutml: i) government policies do not affect the distribution of wealth across households; and ii) if the government decides to tax a household in the second period there is a portfolio available for the banks that generates the Mme payoff in each state of nature as the household taxes. Tben, Ricardian equivalence holds if and only if an appropriate boundary condition is satisfied. Moreover, at every free-entry equilibrium the boundary condition is satisfied and thus Ricardian equivalence holds. These results do not require any particular assumption on the banks' objective function. In particular, we do not assume banks to be risk neutral.

A systematic component of the jump-risk premium in an AJD model

We develop an affine jump diffusion (AJD) model with the jump-risk premium being determined by both idiosyncratic and systematic sources of risk. While we maintain the classical affine setting of the model, we add a finite set of new state variables that affect the paths of the primitive, under both the actual and the risk-neutral measure, by being related to the primitive's jump process. Those new variables are assumed to be commom to all the primitives. We present simulations to ensure that the model generates the volatility smile and compute the "discounted conditional characteristic function'' transform that permits the pricing of a wide range of derivatives.

Limited liability and non-responsiveness in moral hazard and adverse selection problems

This work analyses the optimal menu of contracts offered by a risk neutral principal to a risk averse agent under moral hazard, adverse selection and limited liability. There are two output levels, whose probability of occurrence are given by agent’s private information choice of effort. The agent’s cost of effort is also private information. First, we show that without assumptions on the cost function, it is not possible to guarantee that the optimal contract menu is simple, when the agent is strictly risk averse. Then, we provide sufficient conditions over the cost function under which it is optimal to offer a single contract, independently of agent’s risk aversion. Our full-pooling cases are caused by non-responsiveness, which is induced by the high cost of enforcing higher effort levels. Also, we show that limited liability generates non-responsiveness.

Risk Judgment in Obsessive-Compulsive Disorder: Testing a Dual-Systems Account

Dual-systems theorists posit distinct modes of reasoning. The intuition system reasons automatically and its processes are unavailable to conscious introspection. The deliberation system reasons effortfully while its processes recruit working memory. The current paper extends the application of such theories to the study of Obsessive-Compulsive Disorder (OCD). Patients with OCD often retain insight into their irrationality, implying dissociable systems of thought: intuition produces obsessions and fears that deliberation observes and attempts (vainly) to inhibit. To test the notion that dual-systems theory can adequately describe OCD, we obtained speeded and unspeeded risk judgments from OCD patients and non-anxious controls in order to quantify the differential effects of intuitive and deliberative reasoning. As predicted, patients deemed negative events to be more likely than controls. Patients also took more time in producing judgments than controls. Furthermore, when forced to respond quickly patients' judgments were more affected than controls'. Although patients did attenuate judgments when given additional time, their estimates never reached the levels of controls'. We infer from these data that patients have genuine difficulty inhibiting their intuitive cognitive system. Our dual-systems perspective is compatible with current theories of the disorder. Similar behavioral tests may prove helpful in better understanding related anxiety disorders. (C) 2013 Elsevier Ltd. All rights reserved.

A kockázat megjelenése a származtatott pénzügyi termékekben (The risk appearing in financial derivatives)

A pénzügyi kockázatok szerepe, modellezése, kezelése az utóbbi évtizedekben vált egyre hangsúlyosabbá az elméletben és a gyakorlatban egyaránt. A 2007-ben kezdődő pénzügyi válság egyik kiváltó oka a kockázatok nem megfelelő felmérése volt. A válság egyik tanulsága, hogy bár a matematika és a fizika hozzájárulása rendkívül mély módszertani apparátust biztosított a kockázatok számszerűsítésére, ezen eredmények pénzügyi alkalmazása csak akkor sikeres, ha pontosan értjük a modellek feltételeit és korlátait. Jelen cikk a pénzügyi derivatívák értékelésének alapelveit, valamint a származtatott ügyletekben megjelenő kockázatokat tekinti át, illetve bemutatja azokat a bizonytalansági tényezőket, amelyek megkérdőjelezik az értékelés objektivitását. / === / The modeling and management of financial risks became one of the most important topics of the last decade both in theory and fi nancial practice. The mismanagement of fi nancial risks can be mentioned among the reasons contributing to the eruption of the recent crisis. In order to use successfully the methodology of mathematics and physics in pricing of derivatives, we have to consider the assumptions and limits of the models. This paper introduces the main concepts – no arbitrage pricing and risk neutral valuation – in derivatives’ pricing, then presents and quantifies the risk of some derivative products. I am arguing that the assumptions of the Black–Scholes and Merton model are injured at several points, so the pricing can not be perfectly cleared from all the risk preferences. All those risks, deriving from the difference of the reality and the model are priced in the volatility parameter in the practice.

Adaboost is consistent

The risk, or probability of error, of the classifier produced by the AdaBoost algorithm is investigated. In particular, we consider the stopping strategy to be used in AdaBoost to achieve universal consistency. We show that provided AdaBoost is stopped after n1-ε iterations---for sample size n and ε ∈ (0,1)---the sequence of risks of the classifiers it produces approaches the Bayes risk.