1,720,978 research outputs found
Robust portfolio decisions for financial institutions
No full textThe present paper aims to study a robust-entropic optimal control problem arising in the management of financial institutions. More precisely, we consider an economic agent who manages the portfolio of a financial firm. The manager has the possibility to invest part of the firm's wealth in a classical Black-Scholes type financial market, and also, as the firm is exposed to a stochastic cash flow of liabilities, to proportionally transfer part of its liabilities to a third party as a means of reducing risk. However, model uncertainty aspects are introduced as the manager does not fully trust the model she faces, hence she decides to make her decision robust. By employing robust control and dynamic programming techniques, we provide closed form solutions for the cases of the (i) logarithmic; (ii) exponential and (iii) power utility functions. Moreover, we provide a detailed study of the limiting behavior, of the associated stochastic differential game at hand, which, in a special case, leads to break down of the solution of the resulting Hamilton-Jacobi-Bellman-Isaacs equation. Finally, we present a detailed numerical study that elucidates the effect of robustness on the optimal decisions of both players
Optimal agglomerations in dynamic economics
No full textWe study rational expectations equilibrium problems and social optimum problems in infinite horizon spatial economies in the context of a Ramsey type capital accumulation problem with geographical spillovers. We identify sufficient local and global conditions for the emergence (or not) of optimal agglomeration, using techniques from monotone operator theory and spectral theory in infinite dimensional Hilbert spaces. We show that agglomerations may emerge, with any type of returns to scale (increasing or decreasing) and with the marginal productivity of private capital increasing or decreasing with respect to the spatial externality. This is a fairly general result indicating the importance of the network structure of the spatial externality relative to the properties of the aggregate production function. Our analytical methods can be used to systematically study optimal potential agglomeration and clustering in dynamic economics. © 2014 Elsevier B.V
Spatial externalities and agglomeration in a competitive industry
No full textWe introduce spatial spillovers as an externality in the production function of competitive firms operating within a finite spatial domain under adjustment costs. Spillovers may attenuate with distance and the overall externality could contain positive and negative components with the overall effect being positive. We show that when the spatial externality is not internalized by firms, spatial agglomerations may emerge endogenously in a competitive equilibrium. The result does not require increasing returns at the private or the social level, increasing marginal productivity of private capital with respect to the externality, or location advantages. In fact agglomerations may emerge with decreasing returns to scale, declining marginal productivity of private capital with respect to the externality, and no location advantage. The result depends on the interactions between the structures of production technology and spatial effects as shown in the paper. No agglomerations emerge at the social optimum when spillovers are internalized and diminishing returns both from the private and the social point of view prevail. Numerical experiments with Cobb-Douglas and CES technologies and an isoelastic demand confirm our theoretical predictions. © 2014 Elsevier B.V
RandONets: Shallow networks with random projections for learning linear and nonlinear operators
Full text linkDecision Making Under Model Uncertainty: Fréchet–Wasserstein Mean Preferences
Full text linkAbstract. This paper contributes to the literature on decision making under multiple probabilitymodels
by studying a class of variational preferences. These preferences are defined in
terms of Fr echet mean utility functionals, which are based on the Wasserstein metric in the
space of probabilitymodels. In order to produce ameasure that is the “closest” to all probabilitymodels
in the given set,we find the barycenter of the set. We derive explicit expressions
for the Fr echet–Wasserstein mean utility functionals and show that they can be expressed in
terms of an expansion that provides a tractable link between risk aversion and ambiguity
aversion. The proposed utility functionals are illustrated in terms of two applications. The
first application allows us to define the social discount rate under model uncertainty. In the
second application, the functionals are used in risk securitization. The barycenter in this case
can be interpreted as themodel thatmaximizes the probability that different decisionmakers
will agree on,which could be useful for designing and pricing a catastrophe bond
Robust control of parabolic stochastic partial differential equations under model uncertainty
No full textThe present paper is devoted to the study of robust control problems of parabolic stochastic partial differential equations under model uncertainty. To be more precise, the robust control problem under investigation is expressed as a stochastic differential game in a real separable infinite dimensional Hilbert space. By resorting to the theory of mild solutions, we prove that the elliptic partial differential equation associated with the problem at hand, also known as the Hamilton-Jacobi-Bellman-Isaacs equation, admits a unique solution, which is the value function of the game. Furthermore, we investigate the problem of existence of an optimal control pair that satisfies a saddle point property. Finally, as a demonstration of the proposed approach, we apply our results to the study of a certain robust control problem arising in the spatiotemporal management of natural resources
Spatial externalities, R&D spillovers, and endogenous technological change
No full textForward-looking economic agents operating in a finite continuous geographic area choose how much to innovate
at each point in time and space. Based on this assumption, the present study incorporates spatial interactions in
endogenous growth models, addressing the criticism that such models are inconsistent with empirical evidence.
More specifically, we introduce spatial production spillovers, knowledge diffusion across space, and the capability
for spatial heterogeneity into a standard expanding variety growth model based on R&D. We study the
properties of equilibrium and optimal allocations and argue that the characteristics are different from those of
the non-spatial model, which alter the appropriate policy measures. Finally, we provide numerical examples
demonstrating the importance of spatial dependent policy measures in achieving a balanced regional
development
Rational expectations models: An approach using forward-backward stochastic differential equations
No full textDiffusion models in strongly chaotic Hamiltonian systems
Full text linkThe main subject of this thesis is the long time behaviour of strongly chaotic Hamiltonian systems and whether their behaviour ran be modelled with diffusion processes. The problem of diffusion caused by chaos in a particular area preserving map on the torus, the web map is studied. The formalism is then generalised for the study of diffusion in higher dimensional symplectic maps on the cylinder and general results are obtained. A numerical method for the calculation of diffusion coefficients for chaotic maps is described. Finally, the problem of diffusion in phase space in the case where chaos coexists with structures such as stable islands is studied
- …
