We propose a long term portfolio management method which takes into account a liability. Our approach is based on the LQG (Linear, Quadratic cost, Gaussian) control problem framework and then the optimal portfolio strategy hedges the liability by directly tracking a benchmark process which represents the liability. Two numerical results using empirical data published by Japanese organizations are served: simulations tracking an artificial liability and an estimated liability of Japanese organization. The latter one demonstrates that our optimal portfolio strategy can hedge his or her liability.

We propose a new numerical method for solving the Hamilton-JacobiBellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an implicit method in the field of numerical methods for partial differential equations, and thus it is advantageous in the sense that the stability condition is independent of the discretization parameters. We apply our method to the finite time horizon optimal forest harvesting problem, which considers exiting from the forestry business at a finite time. We show that the behavior of the obtained optimal harvesting strategy of the extended problem coincides with our intuition.

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We propose a model of the dynamics of financial assets based on the mean-field framework. This framework allows us to construct a model which includes the interaction among the financial assets reflecting the market structure. Our study is on the cutting edge in the sense of a microscopic approach to modeling the financial market. To demonstrate the effectiveness of our model concretely, we provide a case study, which is the pricing problem of the European call option with short-time memory noise.