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Asset and liability management under a continuous-time mean-variance optimization framework. (English) Zbl 1151.91493

Summary: Asset and liability (AL) management under the mean–variance criteria refers to an optimization problem that maximizes the expected final surplus subject to a given variance of the final surplus or, equivalently, minimizes the variance of the final surplus subject to a given expected final surplus. We employ stochastic optimal control theory to analytically solve the AL management problem in a continuous-time setting. More specifically, we derive both the optimal policy and the mean–variance efficient frontier by a stochastic linear quadratic control framework. Then, the quality of the derived optimal AL management policy is examined by comparing it with those in the literature. We further discuss consequences of a discrepancy in objectives between equity holders and investors of a mutual fund. Finally, the optimal funding ratio, i.e., the wealth-to-liability ratio, is determined.

MSC:

91G10 Portfolio theory
93E20 Optimal stochastic control
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