Elio Canestrelli

Tourist Carrying Capacity: A Fuzzy Approach

Abstract This paper discusses the concept of tourist-carrying capacity of an urban cultural destination and presents a model for determining its optimal level. The model is then made operational within a “fuzzy” linear programming approach that is tested in the case of the historical center of Venice. The “fuzziness” of the model makes it possible to take into account the distribution of benefits and costs from tourism between the tourist-dependent and the tourist-independent resident populations who confront different categories of tourists and day-trippers.

Tracking error: a multistage portfolio model

Abstract We study multistage tracking error problems. Different tracking error measures, commonly used in static models, are discussed as well as some problems which arise when we move from static to dynamic models. We are interested in dynamically replicating a benchmark using only a small subset of assets, considering transaction costs due to rebalancing and introducing a liquidity component in the portfolio. We formulate and solve a multistage tracking error model in a stochastic programming framework. We numerically test our model by dynamically replicating the MSCI Euro index. We consider an increasing number of scenarios and assets and show the superior performance of the dynamically optimized tracking portfolio over static strategies.

Dynamic portfolio optimization: Time decomposition using the Maximum Principle with a scenario approach

We study a dynamic portfolio management problem over a finite horizon with transaction costs and a risk averse objective function. We assume that the uncertainty faced by the investor can be modelled or approximated using discrete probability distributions via a scenario approach. To solve the resulting optimization problem we use stochastic programming techniques; in particular a scenario decomposition approach. To take advantage of the structure of the portfolio problem we propose a further decomposition obtained by means of a discrete version of the Maximum Principle. The result is a double decomposition of the original problem: The first, given by the scenario approach, focuses on the stochastic aspect of the problem while the second, using the discrete Maximum Principle, concerns the dynamics over time. Applying the double decomposition to our portfolio problem yields a simpler and more direct solution approach which we illustrate with examples.

Current Topics in Quantitative Finance

J. Abaffy, M. Bertocchi, J. Dupacova, V. Moriggia: Performance Evaluation of Algorithms for Black-Derman-Toy Lattice.- M. Bonilla, A. Medal: Efficient Diversification of International Investment: The Spanish Point of View.- E. Canestrelli, S. Giove: Scenarios Identification for Financial Modelling.- M. Corazza: Merton-like Theoretical Frame for Fractional Brownian Motion in Finance.- A. Gamba: Portfolio Analysis with Symmetric Stable Paretian Returns.- T. Pinvanichkul, J.P. Gupta: Dynamics of Bond Returns in the Emerging Markets: A Study of the Thai Bond Market.- W.G. Hallerbach: Modelling Option-Implied Return Distributions: A Generalized Log-Logistic Approximation.- M. Konak: Dichotomous Rate in Stock-Price Process.- A. Resti: How Should We Measure Bank Efficiency? A Comparison of Classic and Recent Techniques Based on Simulated Data.- M.R. Simonelli: The Scheme of Fuzzy Dominance.

Downside Risk in Multiperiod Tracking Error Models

The recent crisis made it evident that replicating the performance of a benchmark is not a sufficient goal to meet the expectations of usually risk-averse investors. The manager should also consider that the investors are seeking downside protection when the benchmark performs poorly and thus they should integrate a form of downside risk control. We propose a multiperiod double tracking error portfolio model which combines these two goals and provides enough flexibility. In particular, the control of the downside risk is carried out through the presence of a floor benchmark with respect to which we can accept different levels of shortfall. The choice of a proper measure for downside risk leads to different problem formulations and investment strategies which can reflect different attitudes towards risk. The proposed model is tested through a set of out-of-sample rolling simulations in different market conditions.

Stability in possibilistic quadratic programming

Abstract We show that possibilistic quadratic programs with crisp decision variables and continuous fuzzy number coefficients are well-posed, i.e. small changes in the membership function of the coefficients may cause only a small deviation in the possibility distribution of the objective function.

Combining stochastic programming and optimal control to decompose multistage stochastic optimization problems

The paper suggests a possible cooperation between stochastic programming and optimal control for the solution of multistage stochastic optimization problems. We propose a decomposition approach for a class of multistage stochastic programming problems in arborescent form (i.e. formulated with implicit non-anticipativity constraints on a scenario tree). The objective function of the problem can be either linear or nonlinear, while we require that the constraints are linear and involve only variables from two adjacent periods (current and lag 1). The approach is built on the following steps. First, reformulate the stochastic programming problem into an optimal control one. Second, apply a discrete version of Pontryagin maximum principle to obtain optimality conditions. Third, discuss and rearrange these conditions to obtain a decomposition that acts both at a time stage level and at a nodal level. To obtain the solution of the original problem we aggregate the solutions of subproblems through an enhanced mean valued fixed point iterative scheme.

Tracking error with minimum guarantee constraints

In recent years the popularity of indexing has greatly increased in financial markets and many different families of products have been introduced. Often these products also have a minimum guarantee in the form of a minimum rate of return at specified dates or a minimum level of wealth at the end of the horizon. Period of declining stock market returns together with low interest rate levels on Treasury bonds make it more difficult to meet these liabilities. We formulate a dynamic asset allocation problem which takes into account the conflicting objectives of a minimum guaranteed return and of an upside capture of the risky asset returns. To combine these goals we formulate a double tracking error problem using asymmetric tracking error measures in the multistage stochastic programming framework.

Local Learning of Tide Level Time Series using a Fuzzy Approach

Forecasting the tide level in the Venezia lagoon is a very compelling task. In this work we propose a new approach to the learning of tide level time series based on the local learning procedure of Bottou and Vapnik, by considering the use of a fuzzy method for the selection of the closest patterns to the one to forecast. We made use also as learners of Support Vector Machines and of their ensembles based on Bagging and AdaBoost. The obtained forecasts of 500 randomly selected tide levels seem to be quite promising. Good performances are also noticed for forecasts of a set of 80 tide levels corresponding to exceptional periods with high tide and sea variabilities. The obtained forecasts of 80 selected tide levels compare very favorably with those of the baseline linear regressor model.

Minimizing a Fuzzy Function

The present paper considers the unconstrained optimization of a continuous fuzzy function with respect to fuzzy numbers of the L-R type. We extend some methods of solution of non-fuzzy parametric mathematical programming to the fuzzy case.