A network of business relations to model counterparty risk

This contribution presents a network of interdependent firms in which the spatial diffusion of the business relations is described by an entropy spatial interaction model. This network is used in a credit risk model in order to take into account the counterparty risk and describe the resulting contagion effects.credit risk contagion, networks, counterparty risk, entropy spatial models

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.Minimum guarantee, benchmark, tracking error, dynamic asset allocation, scenario

Credit contagion in a network of firms with spatial interaction

In this contribution we carried out a wide simulation analysis in order to study the contagion mechanism induced in a portfolio of bank loans by the presence of business relationships among the positions. To this aim we jointly apply a structural model based on a factor approach extended in order to include the presence of microeconomic relationships that takes into account the counterparty risk, and a network model to describe the business connections among interdependent firms. The network of firms is generated resorting to an entropy spatial interaction model.credit risk, bank loan portfolios, contagion models, entropy spatial models

Tracking Error: a multistage portfolio model

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.

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

In this contribution we propose an approach to solve a multistage stochastic programming problem which allows us to obtain a time and nodal decomposition of the original problem. This double decomposition is achieved applying a discrete time optimal control formulation to the original stochastic programming problem in arborescent form. Combining the arborescent formulation of the problem with the point of view of the optimal control theory naturally gives as a first result the time decomposability of the optimality conditions, which can be organized according to the terminology and structure of a discrete time optimal control problem into the systems of equation for the state and adjoint variables dynamics and the optimality conditions for the generalized Hamiltonian. Moreover these conditions, due to the arborescent formulation of the stochastic programming problem, further decompose with respect to the nodes in the event tree. The optimal solution is obtained by solving small decomposed subproblems and using a mean valued fixed-point iterative scheme to combine them. To enhance the convergence we suggest an optimization step where the weights are chosen in an optimal way at each iteration.Stochastic programming, discrete time control problem, decomposition methods, iterative scheme

Time and nodal decomposition with implicit non-anticipativity constraints in dynamic portfolio optimization

We propose a decomposition method for the solution of a dynamic portfolio optimization problem which fits the formulation of a multistage stochastic programming problem. The method allows to obtain time and nodal decomposition of the problem in its arborescent formulation applying a discrete version of Pontryagin Maximum Principle. The solution of the decomposed problems is coordinated through a fixed- point weighted iterative scheme. The introduction of an optimization step in the choice of the weights at each iteration allows to solve the original problem in a very efficient way.Stochastic programming, Discrete time optimal control problem, Iterative scheme, Portfolio optimization

Cumulative Prospect Theory portfolio selection

We introduce elements of Cumulative Prospect Theory into the portfolio selection problem and then compare stock portfolios selected under the behavioral approach with those selected according to classical approaches, such as Mean Variance and Mean Absolute Deviation ones. The mathematical programming problem associated to the behavioral portfolio selection is highly non-linear and non-differentiable; for these reasons it is solved using a Particle Swarm Optimization approach. An application to the STOXX Europe 600 equity market is performed.We introduce elements of Cumulative Prospect Theory into the portfolio selection problem and then compare stock portfolios selected under the behavioral approach with those selected according to classical approaches, such as Mean-Variance and Mean Absolute Deviation ones. The mathematical programming problem associated to the behavioral portfolio selection is highly non-linear and non-differentiable; for these reasons, it is solved using a Particle Swarm Optimization approach. An application to the STOXX Europe 600 equity market is performed

3M cod possible technical measures: spatial / temporal closures

In 2019, the NAFO Commission requested the NAFO Scientific Council (SC) advice on possible technical measures to protect and improve the productivity of the 3M stock of Atlantic cod, Gadus morhua. The objective of this paper is to study possible protection measures related to the temporal and spatial closures of fishing activity. Analysis of historical maturity data indicates that the spawning time of 3M cod occurs during the first quarter of the year and that it is when 65% of the annual cod catch is made. The catch per unit of effort (CPUE) has generally higher values in this season than in the rest of the year and the mean length of caught cod in that season is generally above the length at maturity (L50). During this first quarter, trawl fishery activities are concentrated in a small area at the Southwest of the fishing ground, but, as our data comes from the fishery, we cannot conclude that this is the only spawning area as we have not information about cod activity in the rest of the area in that season. For all these reasons, it is concluded that a spawning closure of Flemish Cap cod fishery during the first quarter of the year may be a suitable measure to protect and improve the productivity of 3M cod stock

MATHEMATICAL METHODS IN ECONOMICS AND FINANCE

Mathematical Methods in Economics and Finance is a journal published by the Ca' Foscari Department of Economics since 2012, and formerly published by the Department of Applied Mathematics of the same University from 2006 to 2011. This journal replaces the former Rendiconti, a series in Italian issued annually from 1969 to 2005. The main features of the journal are: 1. Publication of original and unpublished papers that present theoretical results, methodological contributions, and applications in the areas of actuarial mathematics, financial mathematics, management science, mathematical economics, quantitative finance, and operational research. 2. Peer review process based on double-blind refereeing by at least two anonymous referees. 3. Inclusion in the MathSciNet list of journals. 4. Published papers online are free to access and download

MATHEMATICAL METHODS IN ECONOMICS AND FINANCE

Mathematical Methods in Economics and Finance is a journal published by the Ca' Foscari Department of Economics since 2012, and formerly published by the Department of Applied Mathematics of the same University from 2006 to 2011. This journal replaces the former Rendiconti, a series in Italian issued annually from 1969 to 2005. The main features of the journal are: 1. Publication of original and unpublished papers that present theoretical results, methodological contributions, and applications in the areas of actuarial mathematics, financial mathematics, management science, mathematical economics, quantitative finance, and operational research. 2. Peer review process based on double-blind refereeing by at least two anonymous referees. 3. Inclusion in the MathSciNet list of journals. 4. Published papers online are free to access and download