Distributionally Robust Goal-Reaching Optimization in the Presence of Background Risk

Yichun Chi, Zuo Quan Xu, Sheng Chao Zhuang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

In this article, 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 nonconcave, these two problems bring highly unconventional and challenging issues for which classical optimization techniques often fail. Using a 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.

Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalNorth American Actuarial Journal
DOIs
Publication statusE-pub ahead of print - 7 Oct 2021

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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