Three dimensional quantum key distribution in the presence of several eavesdroppers

Quantum key distribution based on encoding in three dimensional systems in the presence of several eavesdroppers is proposed. This extends the BB84 protocol in the presence of many eavesdroppers where two-level quantum systems (qubits) are replaced by three-level systems (qutrits). We discuss the scenarios involving two, three and four complementary bases. We derive the explicit form of Alice and Bob mutual information and the information gained by each eavesdropper. In particular, we show that, in the presence of only one eavesdropper, the protocol involving four bases is safer than the other ones. However, for two eavesdroppers, the security is strongly dependent on the attack probabilities. The effect of a large number of eavesdroppers is also investigated

Option-Pricing in Incomplete Markets: The Hedging Portfolio plus a Risk Premium-Based Recursive Approach

Consider a non-spanned security C_{T} in an incomplete market. We study the risk/return trade-offs generated if this security is sold for an arbitrage-free price C₀ and then hedged. We consider recursive "one-period optimal" self-financing hedging strategies, a simple but tractable criterion. For continuous trading, diffusion processes, the one-period minimum variance portfolio is optimal. Let C₀(0) be its price. Self-financing implies that the residual risk is equal to the sum of the one-period orthogonal hedging errors, ∑_{t≤T}Y_{t}(0)e^{r(T-t)}. To compensate the residual risk, a risk premium y_{t}Δt is associated with every Y_{t}. Now let C₀(y) be the price of the hedging portfolio, and ∑_{t≤T}(Y_{t}(y)+y_{t}Δt)e^{r(T-t)} is the total residual risk. Although not the same, the one-period hedging errors Y_{t}(0) and Y_{t}(y) are orthogonal to the trading assets, and are perfectly correlated. This implies that the spanned option payoff does not depend on y. Let C₀=C₀(y). A main result follows. Any arbitrage-free price, C₀, is just the price of a hedging portfolio (such as in a complete market), C₀(0), plus a premium, C₀-C₀(0). That is, C₀(0) is the price of the option's payoff which can be spanned, and C₀-C₀(0) is the premium associated with the option's payoff which cannot be spanned (and yields a contingent risk premium of ∑y_{t}Δte^{r(T-t)} at maturity). We study other applications of option-pricing theory as wellOption Pricing; Incomplete Markets

The Structural Approach of a Natrex Model on Equilibrium Exchange Rates

Following a general macroeconomic approach, this paper sets a closed micro-founded structural model to determine the long run real exchange rate of a developed economy. In particular, the analysis follows the structure of a Natrex model. The main contribution of this research paper is the development of a solid theoretical framework that analyse in depth the basis of the real exchange rate and the details of the equilibrium dynamics after any shock influencing the steady state. In our case, the intertemporal factors derived from the stock-flow relationship will be particularly determinant. The main results of the paper can be summarised as follows. In first place, a complete well-integrated structural model for long-run real exchange rate determination is developed from first principles. Moreover, within the concrete dynamics of the model, it is found that some convergence restrictions will be necessary. On one hand, for the medium run convergence the sensitivity of the trade balance to changes in real exchange rate should be higher that the correspondent one to the investment decisions. On the other hand, and regarding long-run convergence, it is also necessary both that there exists a negative relationship between investment and capital stock accumulation and that the global saving of the economy depends positively on net foreign debt accumulation. In addition, there are also interesting conclusions about the effects that certain shocks over the exogenous variables of the model have on real exchange rates.macroeconomic approach, long run real exchange rate, Natrex models, equilibrium dynamics, convergence restrictions, productivity, foreign debt accumulation.

CURRENT ACCOUNT IMBALANCES, THRIFTINESS AND THE REAL EXCHANGE RATE IN A GROWING ECONOMY

This paper analyses the theoretical relevance of the dynamical aspects of growth on the discussion about the observed positive correlation between per capita real income and real exchange rates. With this purpose, we develop a simple exogenous growth model where the internal, external and intertemporal equilibrium conditions of a typical macroeconomic model are imposed; this last one through the inclusion of a balanced growth path for the foreign assets accumulation. The main result under this consideration is that the relationship defended by the Balassa-Samuelson hypothesis is no more so straightforward. In our particular approach, the mentioned bilateral relationship depends on a parameter measuring thriftiness in the economy. Therefore, the probability of ending up with a positive relationship between growth and real exchange rates -as the classical economic theory predicts- will be higher when the economy is able to maintain a minimum saving ratio. Moreover, given that our model considers a simple Keynesian consumption function, some explosive paths can also be possible.Balassa-Samuelson hypothesis, foreign debt, growth, macroeconomic approach, per capita income, real exchange rate, thriftiness

Aging, Gender and Neighbourhood Determinants of Distance Traveled: A Multilevel Analysis in the Hamilton CMA

The objective of this study is to investigate the determinants of mean trip distance traveled by different mode types. The study uses data from the Hamilton CMA in Canada, and multilevel models to investigate demographic aging factors, gender differentials, and neighbourhood attributes on distance traveled. The results of the study validate previous findings regarding the decline in distance traveled as age advances. In addition, it is found that: 1) While this effect of age is present for all modes analyzed (car-driving, car-passenger, and bus) it is considerably more marked for car-driving; 2) There are significant gender effects compounded by the interrelated factors of employment constraints, household dynamics, and greater reliance on travel modes other than car driving; and 3) Neighbourhoods with high commercial and residential mix showed a negative relation with distance traveled only in the case of car-driver.distance traveled, aging, elderly, gender, neighbourhood influence, multilevel analysis

Social Capital and Government in the Production of Public Goods

As a response to the rapidly growing empirical literature on social capital and the evidence of its correlation with government performance, we build a theoretical framework to study the interactions between social capital and government's action. This paper presents a model of homogeneous agents in an overlapping generations framework incorporating social capital as the values transmitted from parent to child. The government's role is to provide public goods. First, government expenditure is exogenously given. Then, it will be chosen at the preferred level of the representative agent. For both setups the equilibrium outcomes are characterized and the resulting dynamics studied. Briefly we include an analysis of the effect of productivity growth on the evolution of social capital. The results obtained caution caution against both the crowding out effect of the welfare state and the impact of sustained economic growth on social capital.Social Capital, Productivity Growth, Government, Public Goods