Differentiable neural substrates for learned and described value and risk.

Studies of human decision making emerge from two dominant traditions: learning theorists [1-3] study choices in which options are evaluated on the basis of experience, whereas behavioral economists and financial decision theorists study choices in which the key decision variables are explicitly stated. Growing behavioral evidence suggests that valuation based on these different classes of information involves separable mechanisms [4-8], but the relevant neuronal substrates are unknown. This is important for understanding the all-too-common situation in which choices must be made between alternatives that involve one or another kind of information. We studied behavior and brain activity while subjects made decisions between risky financial options, in which the associated utilities were either learned or explicitly described. We show a characteristic effect in subjects' behavior when comparing information acquired from experience with that acquired from description, suggesting that these kinds of information are treated differently. This behavioral effect was reflected neurally, and we show differential sensitivity to learned and described value and risk in brain regions commonly associated with reward processing. Our data indicate that, during decision making under risk, both behavior and the neural encoding of key decision variables are strongly influenced by the manner in which value information is presented.

Modeling and forecasting value-at-risk for the Portuguese stock market

The aim of this work project is to find a model that is able to accurately forecast the daily Value-at-Risk for PSI-20 Index, independently of the market conditions, in order to expand empirical literature for the Portuguese stock market. Hence, two subsamples, representing more and less volatile periods, were modeled through unconditional and conditional volatility models (because it is what drives returns). All models were evaluated through Kupiec’s and Christoffersen’s tests, by comparing forecasts with actual results. Using an out-of-sample of 204 observations, it was found that a GARCH(1,1) is an accurate model for our purposes.

Stress testing a complement of value-a-risk.

Rapport de stage (maîtrise en finance mathématique et computationnelle)

Estructura del portafolio de inversiones con el VAR (Valué at Risk)

El propósito general de este trabajo de investigación es el de identificar las herramientas que permitan evaluar riesgos, poder determinar un modelo de ayuda para la estructuración de portafolios y así retribuir al inversionista la mejor manera con un premio por riesgo en retorno de su inversión, Además de presentar un instrumento y demostrar las ventajas de su utilización en la valoración de riesgos en portafolios, se pretende distinguir los efectos económicos y financieros que el inversionista enfrenta. Para cumplir con este propósito, se realizo un diagnóstico y análisis de la actividad de los mercados Financieros y de Capitales, determinando los factores más importantes dentro de un modelo de valoración de riesgo para la estructura de un portafolio de renta variable, lo que me permitirá presentar de una manera clara, los aspectos técnicos y económicos que afectan a la estructura de una inversión aplicando la metodología denominada VAR (Valué at Risk); adicionalmente el manejo que se podría dar a las mismas para obtener un mayor beneficio. Los resultados obtenidos y su respectivo análisis constan a lo largo de este trabajo de investigación.

Parametric preference functionals under risk in the gain domain: a Bayesian analysis

The performance of rank dependent preference functionals under risk is comprehensively evaluated using Bayesian model averaging. Model comparisons are made at three levels of heterogeneity plus three ways of linking deterministic and stochastic models: the differences in utilities, the differences in certainty equivalents and contextualutility. Overall, the"bestmodel", which is conditional on the form of heterogeneity is a form of Rank Dependent Utility or Prospect Theory that cap tures the majority of behaviour at both the representative agent and individual level. However, the curvature of the probability weighting function for many individuals is S-shaped, or ostensibly concave or convex rather than the inverse S-shape commonly employed. Also contextual utility is broadly supported across all levels of heterogeneity. Finally, the Priority Heuristic model, previously examined within a deterministic setting, is estimated within a stochastic framework, and allowing for endogenous thresholds does improve model performance although it does not compete well with the other specications considered.

Non-smooth optimization methods for computation of the conditional value-at-risk and portfolio optimization

We examine numerical performance of various methods of calculation of the Conditional Value-at-risk (CVaR), and portfolio optimization with respect to this risk measure. We concentrate on the method proposed by Rockafellar and Uryasev in (Rockafellar, R.T. and Uryasev, S., 2000, Optimization of conditional value-at-risk. Journal of Risk, 2, 21-41), which converts this problem to that of convex optimization. We compare the use of linear programming techniques against a non-smooth optimization method of the discrete gradient, and establish the supremacy of the latter. We show that non-smooth optimization can be used efficiently for large portfolio optimization, and also examine parallel execution of this method on computer clusters.