Distributionally robust goal-reaching optimization in the presence of background risk
In this paper, we examine the effect of background risk on portfolio selection and optimal reinsurance design under the criterion of maximizing the probability of reaching a goal. Following the literature, we adopt dependence uncertainty to model the dependence ambiguity between financial risk (or insurable risk) and background risk. Because the goal-reaching objective function is non-concave, these two problems bring highly unconventional and challenging issues for which classical optimization techniques often fail. Using quantile formulation method, we derive the optimal solutions explicitly. The results show that the presence of background risk does not alter the shape of the solution but instead changes the parameter value of the solution. Finally, numerical examples are given to illustrate the results and verify the robustness of our solutions.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Hedging Goals
Goal-based investing is concerned with reaching a monetary investment goal by a given finite deadline, which differs from mean-variance optimization in modern portfolio theory. In this article, we expand the close connec…
Efficient Probabilistic Planning with Maximum-Coverage Distributionally Robust Backward Reachable Trees
This paper presents a new multi-query motion planning algorithm for linear Gaussian systems with the goal of reaching a Euclidean ball with high probability. We develop a new formulation for ball-shaped ambiguity sets of…
Motion PlanningDistributionally Robust Bayesian Optimization
Robustness to distributional shift is one of the key challenges of contemporary machine learning. Attaining such robustness is the goal of distributionally robust optimization, which seeks a solution to an optimization p…
Bayesian OptimizationDistributionally Robust Post-hoc Classifiers under Prior Shifts
The generalization ability of machine learning models degrades significantly when the test distribution shifts away from the training distribution. We investigate the problem of training models that are robust to shifts …
Wasserstein Distributionally Robust Bayesian Optimization with Continuous Context
We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions …
Bayesian OptimizationDecision Making