A. N. Yannacopoulos

A probabilistic model for optimal insurance contracts against security risks and privacy violation in IT outsourcing environments

Day by day the provision of information technology goods and services becomes noticeably expensive. This is mainly due to the high labor cost for the service providers, resulting from the need to cover a vast variety of application domains and at the same time to improve or/and enhance the services offered in accordance to the requirements set by the competition. A business model that could ease the problem is the development or/and provision of the service by an external contractor on behalf of the service provider; known as Information Technology Outsourcing. However, outsourcing a service may have the side effect of transferring personal or/and sensitive data from the outsourcing company to the external contractor. Therefore the outsourcing company faces the risk of a contractor who does not adequately protect the data, resulting to their non-deliberate disclosure or modification, or of a contractor that acts maliciously in the sense that she causes a security incident for making profit out of it. Whatever the case, the outsourcing company is legally responsible for the misuse of personal data or/and the violation of an individual’s privacy. In this paper we demonstrate how companies adopting the outsourcing model can protect the personal data and privacy of their customers through an insurance contract. Moreover a probabilistic model for optimising, in terms of the premium and compensation amounts, the insurance contract is presented.

On the approximate controllability of the stochastic Maxwell equations

We study the approximate controllability of the stochastic Maxwell equations with an abstract approach and a constructive approach using a generalization of the Hilbert uniqueness method as proposed in Kim (2004, Approximate controllability of a stochastic wave equation. Appl. Math. Optim., 49, 81–98) for the stochastic wave equation.

Optimal switching decisions under stochastic volatility with fast mean reversion

We study infinite-horizon, optimal switching problems for underlying processes that exhibiting “fast” mean-reverting stochastic volatility. We obtain closed-form analytic approximations of the solution for the resulting quasi-variational inequalities, that provide quantitative and qualitative results for the effects of multi-scale variability of the underlying process on the optimal switching rule. The proposed methodology is applicable to a number of operations research problems involving switching flexibility.

Stochastic integrodifferential equations in Hilbert spaces with applications in electromagnetics

In this work we present some results on deterministic and stochastic integrodifferential equations in Hilbert spaces, motivated from and applied to problems arising from the mathematical modeling of electromagnetics fields in complex random media. We examine the mild, strong and classical well posedness for the Cauchy problem of the integrodifferential equation which describes Maxwell’s equations complemented with the general (and therefore nonlocal in time) linear constitutive relations describing such media, with either additive or multiplicative noise.

Scenarios for Price Determination in Incomplete Markets

We study the problem of determination of asset prices in an incomplete market proposing three different but related scenarios, based on utility pricing. One scenario uses a market game approach whereas the other two are based on risk sharing or regret minimizing considerations. Dynamical schemes modeling the convergence of the buyer and seller prices to a unique price are proposed. The case of exponential utilities is treated in detail, in the simplest possible example of an incomplete market, the trinomial model.

Robust Control and Hot Spots in Spatiotemporal Economic Systems

We formulate stochastic robust optimal control problems, motivated by applications arising in interconnected economic systems, or spatially extended economies. We study in detail linear quadratic problems and nonlinear problems. We derive optimal robust controls and identify conditions under which concerns about model misspecification at specific site(s) could cause regulation to break down, to be very costly, or to induce pattern formation and spatial clustering. We call sites associated with these phenomena hot spots. We also provide an application of our methods by studying optimal robust control and the potential break down of regulation, due to hot spots, in a model where utility for in situ consumption is distance dependent.

The Bioeconomics of Migration: A Selective Review Towards a Modelling Perspective

We present a selective review of migration and its connection with the economy, focusing on issues leading towards a modelling perspective. We introduce a class of models based on difference equations on directed graphs that may provide a quantitative and qualitative description of human migration and present some of their bioeconomic, mathematical and simulation challenges.

On a variational sequential bargaining pricing scheme

Abstract We propose a minimization problem as a model for the interaction between two agents trading a contingent claim in an incomplete discrete-time multiperiod financial market. The agents personal valuations for the contingent claim are assumed to depend on probability measures representing their beliefs concerning the future states of the world. The agents’ goal is to achieve a common price for the contingent claim to be traded, while deviating as litle as possible from their initial beliefs. Under appropriate conditions, we prove that the minimization problem under consideration admits at least one solution. Furthermore, we provide a detailed description for the minimizers – orbits of a finite horizon discrete-time dynamical system on the space of probability measures representing the agents beliefs.

A projected gradient dynamical system modelling the dynamics of bargaining

We propose a projected gradient dynamical system as a model for a bargaining scheme for an asset for which the two interested agents have personal valuations that do not initially coincide. The personal valuations are formed using subjective beliefs concerning the future states of the world, and the reservation prices are calculated using expected utility theory. The agents are not rigid concerning their subjective probabilities and are willing to update them under the pressure to reach finally an agreement concerning the asset. The proposed projected dynamical system, on the space of probability measures, provides a model for the evolution of the agents, beliefs during the bargaining period and is constructed so that an agreement is reached under the minimum possible deviation of both agents from their initial beliefs. The convergence results are shown using techniques from convex dynamics and Lyapunov function theory.

Stochastic Models for the Lexical Richness of a Text: Qualitative Results

In this paper we propose a stochastic model for the study of lexical richness of a text based on the introduction of the concept of elasticity. We set certain properties that a successful model of lexical richness should have and using the theory of stochastic differential equations we provide criteria that will allow researchers to check whether a particular model passes possesses these properties or not.