Asset and liability management: A stochastic control approach

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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.