Asset and liability management: A stochastic control approach

资产和负债管理：随机控制方法

• 批准号: RGPIN-2016-05677
• 负责人: Shen, Yang
• 金额: $ 1.46万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=709924
• 关键词: Asset; liability; management; stochastic; control

Imagine that an institutional investor manages a business or an individual investor faces the problem of life-cycle planning so that assets are well invested to cover liabilities. Asset and liability management (in short, ALM) is a general concept of coordinating assets and liabilities in a unified framework. It is at the crossroads between risk management and strategic planning. ALM is not only about hedging or mitigating the underlying risks but is focused on boosting the long-term returns. Indeed, the modern view of the ALM programs is to balance the relationships among risks, costs and returns. Traditionally, interest rate risk and liquidity risk were dominant risk factors in the practice of asset-liability management. Introduced by the actuary F.M. Redington in 1952, interest rate immunization used to be a main tool in ALM. However, the idea of perfect matching in immunization, though effective, may not always be efficient. In recent years, worldwide financial markets have evolved to be much more complicated. The scope of ALM has been largely widened to address new risk factors, such as equity risk, currency risk, inflation risk and mortality risk. The proposed research intends to develop a systematic and integrated approach to ALM with numerous risk factors and different objectives being taken into account. A stochastic control approach will be employed to study several problems related to ALM. The research relies on powerful tools coming from stochastic control theory, such as linear-quadratic control, stochastic maximum principle, martingale optimality principle and backward stochastic differential equations. The novelty of the research program lies in providing a general framework with non-Markovian random coefficients and different objective functions to various stochastic control/differential game problems in ALM. New existence and uniqueness results of backward stochastic differential equations will be derived. Expected outcomes of the research program would be of direct interest to both large institutional investors (namely, pension funds, mutual funds, insurance companies, etc.) and individuals with on-going liability commitments as well as having significant mathematical interest.

想象一下，管理一家企业的机构投资者或个人投资者面临生命周期规划的问题，以便充分投资资产以偿还负债。资产负债管理（简称ALM）是在统一框架内协调资产和负债的总体概念。它处于风险管理和战略规划的十字路口。 ALM 不仅是为了对冲或减轻潜在风险，还着眼于提高长期回报。事实上，ALM 计划的现代观点是平衡风险、成本和回报之间的关系。 传统上，利率风险和流动性风险是资产负债管理实践中的主要风险因素。由精算师F.M.介绍Redington于1952年提出，利率免疫曾经是ALM的主要工具。然而，免疫完美匹配的理念虽然有效，但并不总是有效。近年来，全球金融市场变得更加复杂。 ALM 的范围已大幅扩大，以应对新的风险因素，例如股票风险、货币风险、通货膨胀风险和死亡风险。 拟议的研究旨在开发一种系统的、综合的 ALM 方法，其中考虑了众多风险因素和不同的目标。将采用随机控制方法来研究与 ALM 相关的几个问题。该研究依赖于随机控制理论的强大工具，例如线性二次控制、随机极大值原理、鞅最优原理和向后随机微分方程。 该研究项目的新颖之处在于为ALM中的各种随机控制/微分博弈问题提供了一个具有非马尔可夫随机系数和不同目标函数的通用框架。推导逆向随机微分方程新的存在唯一性结果。研究计划的预期结果将直接引起大型机构投资者（即养老基金、共同基金、保险公司等）和具有持续责任承诺以及对数学有浓厚兴趣的个人的直接兴趣。