Robust utility functionals arise as numerical representations of investor preferences, when the investor is uncertain about the underlying probabilistic model and averse against both risk and model uncertainty. In this paper, we study the the duality theory for the problem of maximizing the robust utility of the terminal wealth in a general incomplete market model. We also allow for very genera...

We prove three theorems about solutions of $\Delta u + e^{2u} = 0$ in the plane. The first two describe explicitly all concave and quasiconcave solutions. third theorem says that diameter plane with respect to metric line element $e^{u}|dz|$ is at least $4\pi/3$, except for described families u.

In this paper, the existence and multiplicity of positive solutions for a critical singular elliptic system with concave and convex nonlinearity and sign-changing weight function, are established. With the help of the Nehari manifold, we prove that the system has at least two positive solutions via variational methods.

We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents. With the help of the Nehari manifold, we prove that the system admits at least two positive solutions when the pair of parameters (λ, μ) belongs to a suitable subset of R.

In this article, we consider the multiplicity of positive solutions for a class of Kirchhoff type problems with concave and convex nonlinearities. Under appropriate assumptions, we prove that the problem has at least two positive solutions, moreover, one of which is a positive ground state solution. Our approach is mainly based on the Nehari manifold, Ekeland variational principle and the theor...

Denote by Ln the projection operator obtained by applying the Lagrange interpolation method, weighted by (1 − x), at the zeros of the Chebyshev polynomial of the second kind of degree n + 1. The norm ‖Ln‖ = max ‖f‖∞≤1 ‖Lnf‖∞, where ‖ · ‖∞ denotes the supremum norm on [−1, 1], is known to be asymptotically the same as the minimum possible norm over all choices of interpolation nodes for unweight...

We provide a revealed preference characterization of expected utility maximization in binary lotteries with prize-probability trade-offs. start by characterizing optimizing behavior when the empirical analyst exactly knows function or probability winning. Next, we consider situation both and unknown. In this case has content imposing mild shape restriction that at least one these functions is l...

In this paper the problem of minimum cost communication network design is considered where the costs are piecewise linear concave. Several methods are compared: Simulated Annealing method, a heuristic based on the method proposed by Minoux, and a lagrangian method based on lower bounding procedure.

In this article, we develop automated inference methods for “local” parameters in a collection of convexity constrained models based on the natural tuning-free estimators. A canonical example is given by univariate convex regression model, which drawn function value, derivative at fixed interior point, and anti-mode function, widely used tuning-free, piecewise linear least squares estimator (LS...