Efficient and robust optimization approaches for financial applications

在金融应用领域，具有计算挑战性的优化问题越来越多。首先，在保险业中，随机情景下的风险管理策略是一个越来越重要的领域。这里的挑战是双重的：如何用优化的语言正确地表达问题，以及如何着眼于效率（计算上可行！）和鲁棒性。我将开发和研究新的（最佳）动态对冲策略，以应对主要的复杂风险，包括隔离（变额年金）保险合同的基差风险和退保风险。其次，我将研究计算涉及对冲基金的投资组合的最佳投资策略。这是一个非常具有挑战性的问题，原因有几个，包括数据的稀缺性和对冲基金回报率分布的非正态性。传统的（基于股权的）投资组合策略是不合适的。然而，鉴于机构和个人投资者越来越有兴趣通过投资对冲基金使其投资组合多样化，迫切需要在这一问题上取得进展。我们将研究这个问题的鲁棒性，但计算上可行的优化方法。

Computationally challenging optimization problems are increasingly arising in the area of finance applications. I propose to work on two important examples.Firstly, in the insurance industry, risk management strategies under stochastic scenarios is an area of growing importance. The challenge here is twofold: how to properly formulate the problems in the language of optimization, and how to solve the resulting problems with an eye toward efficiency (computationally feasible!) and robustness. I will develop and investigate new (optimal) dynamic hedging strategies accounting for major complex risks including basis risk and surrender risk of segregated (variable annuity) insurance contracts.Secondly, I will examine the area of computing optimal investment strategies for portfolios involving hedge funds. This is a very challenging problem  for several reasons including scarcity of data and non-normality of the hedge fund return distributions. Traditional (equity-based) portfolio strategies are inappropriate. However, progress on this problem is urgently needed given the increased interest by both institutional and individual investors in diversifying their portfolios by investing in hedge funds. We will investigate robust, but computationally feasible, optimization approaches for this problem.