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We analyze the limiting behavior of the risk premium associated with the Pareto optimal risk sharing contract in an infinitely expanding pool of risks under a general class of law-invariant risk measures encompassing rank-dependent utility…
We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai and Fukasawa (2014). The upper and lower bounds of a good…
We consider the problem of fairly allocating indivisible public goods. We model the public goods as elements with feasibility constraints on what subsets of elements can be chosen, and assume that agents have additive utilities across…
Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems,…
When deploying a single predictor across multiple subpopulations, we propose a fundamentally different approach: interpreting group fairness as a bargaining problem among subpopulations. This game-theoretic perspective reveals that existing…
In this paper we consider reinsurance or risk sharing from a macroeconomic point of view. Our aim is to find socially optimal reinsurance treaties. In our setting we assume that there are $n$ insurance companies each bearing a certain risk…
The purpose of this work is to develop and study a distributed strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the expectation of some loss function with unknown probability…
Decision-makers often have access to machine-learned predictions about future demand that can help guide online resource allocation decisions. However, such predictions may be inaccurate. We develop a framework for online resource…
In this paper, we propose a predictor-corrector type Consensus Based Optimization (CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the…
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
This paper considers the constrained portfolio optimization in a generalized life-cycle model. The individual with a stochastic income manages a portfolio consisting of stocks, a bond, and life insurance to maximize his or her consumption…
This paper studies a dynamic optimal reinsurance and dividend-payout problem for an insurance company in a finite time horizon. The goal of the company is to maximize the expected cumulative discounted dividend payouts until bankruptcy or…
Based on a point of view that solvency and security are first, this paper considers regular-singular stochastic optimal control problem of a large insurance company facing positive transaction cost asked by reinsurer under solvency…
In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A…
This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…
We expose a theoretical hedging optimization framework with variational preferences under convex risk measures. We explore a general dual representation for the composition between risk measures and utilities. We study the properties of the…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
This paper examines an optimal investment problem in a continuous-time (essentially) complete financial market with a finite horizon. We deal with an investor who behaves consistently with principles of Cumulative Prospect Theory, and whose…
This paper considers the difference of stop-loss payoffs where the underlying is a difference of two random variables. The goal is to study whether the comonotonic and countermonotonic modifications of those two random variables can be used…
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…