演講訊息 TALKS

We consider a market model where risky securities are affected by ``hidden'' economic factors, which evolve as a finite-state Markov chain. Our problem is optimizing an expected risk-averse power utility of wealth on finite and infinite time horizons. We will explain that the problem is reduced to a certain stochastic control problem of complete observation. By Bellman's dynamic programming principle, we (formally) derive the Hamilton-Jacobi-Bellman (HJB) equation corresponding to the problem. The HJB equation turns out to be a second order quasilinear degenerate parabolic (elliptic) equation. Under some assumptions, we construct a classical solution of the HJB equation using a probabilistic argument.