Total risk aversion, stochastic optimal control, and differential games

摘要

We present a connection between the theory of risk in the context of a stochastic optimal control problem and its relation to the theory of differential games. In particular, we define the notion of “total risk aversion” from the viewpoint of the upper value of a differential game. We prove that as the index of absolute risk aversion of a utility function in a stochastic control problem converges to infinity the (certainty equivalent) optimal payoff converges to the upper value of an associated deterministic differential game. The two main points of this paper are (1) a precise characterization oftotal risk aversionand (2) the construction of a stochastic optimal control problem intimately connected to a deterministic differential g