Abstract. A risk-averse insurance company controls its reserve, modelled as a perturbed Cramér-Lundberg process, by choice of both the premium p and the deductible K offered to potential customers. The surplus is allocated to financial investment in a riskless and a basket of risky assets potentially correlating with the insurance risks and thus serving as a partial hedge against these. Assuming customers differ in riskiness, increasing p or K reduces the number of customers n(p,K) and increases the arrival rate of claims per customer λ(p,K) through adverse selection, with a combined negative effect on the aggregate arrival rate n(p,K)λ(p,K). We derive the optimal premium rate, deductible, investment strategy, and dividend payout rate (consumption by the owner-manager) maximizing expected discounted life-time utility of intermediate consumption under the assumption of constant absolute risk aversion. Closed-form solutions are provided under specific assumptions on the distributions of size and frequency claims. "Peso problems in the estimation of the C-CAPM" [Online Appendix] [CEPR Working Paper DP16299] with Olaf Posch and Andreas Schrimpf Quantitative Economics(accepted for publication)
Abstract. This paper shows that the consumption-based capital asset pricing model (C-CAPM) with low-probability disaster risk rationalizes pricing errors. We find that implausible estimates of risk aversion and time preference are not puzzling if market participants expect a future catastrophic change in fundamentals, which just happens not to occur in the sample (a ‘peso problem’). A bias in structural parameter estimates emerges as a result of rational pricing errors in quiet times. While the bias essentially removes the pricing error in the simple models with constant risk-free rates, time-variation may also generate large and persistent estimated pricing errors in simulated data. We also show analytically how the problem of biased estimates can be avoided in empirical research by resolving the misspecification in moment conditions.
Abstract. This study evaluates the accuracy of a set of techniques that approximate the solution of continuous-time Dynamic Stochastic General Equilibrium models. Using the neoclassical growth model, I compare linear-quadratic, perturbation, and projection methods. All techniques are applied to the Hamilton–Jacobi–Bellman equation and the optimality conditions that define the general equilibrium of the economy. Two cases are studied depending on whether a closed-form solution is available. I also analyze how different degrees of non-linearities affect the approximated solution. The results encourage the use of perturbations for reasonable values of the structural parameters of the model and suggest the use of projection methods when a high degree of accuracy is required.
Abstract. We show that the sensitivity of the real exchange rate to terms of trade shocks is greater the lower the elasticity of final and derived demand between domestic and imported items. We develop a novel Kalman filter-based method to estimate these key parameters for Colombia, taking account of preference shifts, technological relative price trends and errors in sectoral data. We find that the elasticity of the input of the distribution sector in transforming imports from domestic consumption reliably indicates complementarity, implying that rigidities in this sector matter in determining the sensitivity of the Colombian economy to external shocks.
"La tasa de interés natural en Colombia" ("The natural rate of interest in Colombia") with J.J. Echavarría, M. Misas, E. López and J. Tellez Ensayos Sobre Política Económica (2007), No. 54, pp.44-89
Abstract. In this article we estimate the natural real rate of interest (NRI) in Colombia for 1982 to 2005 based on the methodologies proposed by Laubach and Williams (2001) and Méssonier and Renne (2004). The NRI is estimated as a time varying latent variable within a Kalman Filter alongside the output gap. A Keynesian framework is used to identify these variables. The results suggest that monetary policy was contractionary in 1998 and 1999, and relatively expansive in recent years. The output gap has been positive in 2003 and 2004, confirming the results of of ther research.