Asset and liability management: A stochastic control approach

想象一下，一个机构投资者管理着一家企业，或者一个个人投资者面临着生命周期规划的问题，以便资产得到良好的投资以覆盖负债。资产负债管理（Asset and Liability Management，简称ALM）是在一个统一的框架内协调资产和负债的一般概念。它处于风险管理和战略规划之间的十字路口。资产负债管理不仅仅是对冲或减轻潜在风险，而是专注于提高长期回报。事实上，资产负债管理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. Redington在1952年提出的利率免疫法曾经是资产负债管理的主要工具。然而，完美匹配免疫的想法，虽然有效，但并不总是有效的。近年来，全球金融市场变得更加复杂。资产负债管理的范围已大幅扩大，以应对新的风险因素，如股票风险、货币风险、通胀风险和死亡风险。 拟议的研究旨在制定一个系统的和综合的方法，以资产负债管理与众多的风险因素和不同的目标被考虑在内。随机控制方法将被用来研究与应用层组播相关的几个问题。该研究依赖于随机控制理论的有力工具，如线性二次控制、随机最大值原理、鞅最优性原理和倒向随机微分方程。 该研究方案的新奇之处在于提供了一个通用的框架与非马尔可夫随机系数和不同的目标函数，各种随机控制/微分对策问题在ALM。得到了倒向随机微分方程解的存在唯一性的新结果。研究计划的预期成果将直接关系到大型机构投资者（即养老基金、共同基金、保险公司等）的利益。以及具有持续负债承诺以及具有重大数学兴趣的个人。

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.