Related papers: Optimal Risk Sharing Without Preference Convexity:…
In this paper, we deal with risk evaluation and risk-averse optimization of complex distributed systems with general risk functionals. We postulate a novel set of axioms for the functionals evaluating the total risk of the system. We derive…
We consider the problem of navigation with safety constraints. The safety constraints are probabilistic, where a given set is assigned a degree of safety, a number between zero and one, with zero being safe and one being unsafe. The…
We consider the problem of optimal risk sharing in a pool of cooperative agents. We analyze the asymptotic behavior of the certainty equivalents and risk premia associated with the Pareto optimal risk sharing contract as the pool expands.…
In a Markovian stochastic volatility model, we consider financial agents whose investment criteria are modelled by forward exponential performance processes. The problem of contingent claim indifference valuation is first addressed and a…
Stochastic Model Predictive Control addresses uncertainties by incorporating chance constraints that provide probabilistic guarantees of constraint satisfaction. However, simultaneously optimizing over the risk allocation and the feedback…
We consider the problem of computing optimal linear control policies for linear systems in finite-horizon. The states and the inputs are required to remain inside pre-specified safety sets at all times despite unknown disturbances. In this…
Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This…
Probabilistic risk aversion, defined through quasi-convexity in probabilistic mixtures, is a common useful property in decision analysis. We study a general class of non-monotone mappings, called the generalized rank-dependent functions,…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
Optimization of conditional convex risk measure is a central theme in dynamic portfolio selection theory, which has not yet systematically studied in the previous literature perhaps since conditional convex risk measures are neither random…
The most commonly accepted model for investors' preferences is expected utility theory. More recently, other theories have emerged and pose new challenges to mathematics. The present paper treats preferences of cumulative prospect theory…
In this paper, a novel distributed optimization framework has been proposed. The key idea is to convert optimization problems into optimal control problems where the objective of each agent is to design the current control input minimizing…
We find the optimal indemnity to maximize the expected utility of terminal wealth of a buyer of insurance whose preferences are modeled by an exponential utility. The insurance premium is computed by a convex functional. We obtain a…
Applications such as employees sharing office spaces over a workweek can be modeled as problems where agents are matched to resources over multiple rounds. Agents' requirements limit the set of compatible resources and the rounds in which…
Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The…
In this paper we introduce a generalization of classical risk measures in which the risk is represented by a step function taking two values, corresponding to two endogenously determined market regimes. This extends the traditional…
A fruitful idea, when providing subdifferential formulae and dual representations for convex risk measures, is to make use of the conjugate duality theory in convex optimization. In this paper we underline the outstanding role played by the…
The objective of this paper is to investigate the connection between penalty functions from stochastic optimal control, convex semigroups from analysis and convex expectations from probability theory. Our main result provides a one-to-one…
This technical note studies the distributed optimization problem of a sum of nonsmooth convex cost functions with local constraints. At first, we propose a novel distributed continuous-time projected algorithm, in which each agent knows its…
Many economic models include random shocks imposed on a large number (continuum) of economic agents with individual risk. In this context, an exact law of large numbers and its converse is presented in Sun (2006) to characterize the…