主講者:	1.Prof. Kiyoshi Kawazu (真理大學) 2.Dr. Hiroaki Hata (中央研究院)
講題:	1.On the maximum of a diffusion process in a drifted Brownian environment 2.An optimal consumption problem with linear Gaussian model
時間:	2009-06-18 (Thu.)  10:30 - 15:00
地點:
Abstract:	1.In this talk, we discuss asymptptic behavior of the distribution of the maximum of a diffusion process in a drifted Brownian environment. And we report the asymptotic behavior of the process itself. We consider a diffusion process in random environment {W(x) +cx, x in R}, where W(x) is a standard Wiener process and c is a constant. So the process which we discuss is the one described as dX(t) = dB(t) -1/2 (W'(X(t)) +c )dt with Brownian motion { B(t), t in [ 0 , ∞）} that is independent of {W(x) x in R }. 2.We consider an optimal consumption problem where an investor tries to maximize the infinite horizon expected discounted hyperbolic absolute risk aversion (HARA) utility of consumption. We treat a stochastic factor model that the mean returns of risky assets depend on linearly on underlying economic factors formulated as the solutions of linear stochastic differential equations. Using a dynamic programming principle, we derive the Hamilton-Jacobi-Bellman(HJB) equation. We adopt the subsolution-supersolution method to obtain the existence of solutions of the HJB equation. The optimal investment and consumption policies can be obtained by the solution of the HJB equation. (Joint work with Shuenn-Jyi Sheu )
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