Dynamic asset management with risk-sensitive criterion and non-negative factor constraints: a differential game approach

Abstract

In this paper, we study continuous time portfolio optimization problem where individual securities are directly affected by economic factors. We consider the risksensitive criterion function as is familiar in the robust control literature. This is the natural setting for studying the infinite horizon case of the control problem arising in portfolio optimization. Our result extends earlier works by imposing explicitly the nonnegativity constraint on the economic factors. This is achieved by using reflected diffusions. The risk-sensitive control problem with reflected diffusion is then converted into a stochastic differential game. The lower value of this game leads immediately to the desired optimal strategy. Also we prove the existence of unique strong solution to reflected diffusions with bounded measurable drift coefficient which is the first result of its kind for higher dimensional reflected diffusions.

A nonzero-sum risk-sensitive stochastic differential game in the orthant

“…Under the assumptions (A0) and (A1), for a given (v 1 , v 2 ) ∈ A 1 × A 2 , it has been proved in [7] that (1) has a unique weak solution. Adapting the approach by Zvonkin and Veretenikov (see for example [42]) one can prove that, under a pair of Markov strategies, (1) admits a unique strong solution.…”

“…Adapting the approach by Zvonkin and Veretenikov (see for example [42]) one can prove that, under a pair of Markov strategies, (1) admits a unique strong solution. For more details see [Theorem 3.2, [7]].…”

Assets Management Around Urban Rail Transit

“…And some are concentrating efforts on non-physical assets, they usually give some theoretical suggestions. For both parts, the assets management is not perfect integrated (Bagchi and Kumar, 2009).…”