We introduce a moving average summability method, which is proved to be equivalent with the logarithmic ℓ-method. Several equivalence and Tauberian theorems are given. A strong law of large numbers is also proved.
In this paper, we consider the problem of optimal control for a class of nonlinear stochastic systems with multiplicative noise. The nonlinearity consists of quadratic terms in the state and control variables. The optimality criteria are of a risk-sensitive and generalised risk-sensitive type. The optimal control is found in an explicit closed-form by the completion of squares and the change of measure methods. As applications, we outline two special cases of our results. We show that a subset of the class of models which we consider leads to a generalized quadratic affine term structure model (QATSM) for interest rates. We also demonstrate how our results lead to generalisation of exponential utility as a criterion in optimal investment.
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