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This is the second of two works concerning the Sobolev calculus on metric measure spaces and its applications. In this work, we focus on several approaches to vector calculus in the non-smooth setting of complete and separable metric spaces…
This article studies the problem of utility maximization in an incomplete market under a class of nonlinear expectations and general constraints on trading strategies. Using a $g$-martingale method, we provide an explicit solution to our…
In exponential semi-martingale setting for risky asset we estimate the difference of prices of options when initial physical measure $P$ and corresponding martingale measure $Q$ change to $\tilde{P}$ and $\tilde{Q}$ respectively. Then, we…
In this note we explore duality in reverse convex optimization with reverse convex inequality constraints. While we are examining the special case of a finite index set of the inequality constraints, we are primarily interested in the…
Mean-deviation models, along with the existing theory of coherent risk measures, are well studied in the literature. In this paper, we characterize monotonic mean-deviation (risk) measures from a general mean-deviation model by applying a…
Although the specific structures of electricity markets are diverse around the world, they were all conceived on the premise of predictable, controllable generation with nonnegligible marginal costs. Recent changes, specifically, the…
We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the…
Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…
In the context of Risk Neutral Pricing theory, we consider the classic problem of calibrating a martingale over $\mathbb{R}^n$ to a finite number of marginals thereof, or more practically, to prices of an arbitrary finite set of (joint)…
We consider the problem of finite-horizon optimal control design under uncertainty for imperfectly observed discrete-time systems with convex costs and constraints. It is known that this problem can be cast as an infinite-dimensional convex…
Motivated by applications requiring sparse or nonnegative controls, we investigate reachability properties of linear infinite-dimensional control problems under conic constraints. Relaxing the problem to convex constraints if the initial…
We consider a generalization of the multiple measurement vector (MMV) problem, where the measurement matrices are allowed to differ across measurements. This problem arises naturally when multiple measurements are taken over time, e.g., and…
Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known $\mathcal{S}$-lemma. However, the…
We consider the problem of representing claims for coherent risk measures. For this purpose we introduce the concept of (weak and strong) time-consistency with respect to a portfolio of assets, generalizing the one defined by Delbaen. In a…
In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a…
Convex duality for two two different super--replication problems in a continuous time financial market with proportional transaction cost is proved. In this market, static hedging in a finite number of options, in addition to usual dynamic…
We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a…
In this paper, we study convex risk measures with weak optimal transport penalties. In a first step, we show that these risk measures allow for an explicit representation via a nonlinear transform of the loss function. In a second step, we…