Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1153049 | Statistics & Probability Letters | 2010 | 5 Pages |
Abstract
We consider a problem of optimally controlling a two-dimensional diffusion process dxtμ,β=μ(xt)dt+β(xt)dBt1;x(0)=x,dyt=αytdt+(Ïxt+γ)ytdBt2;y(0)=y, initially starting in the interior of a domain DÏ={(x,y)âR+2:Ï(x)0 and θ>1 are fixed positive constants and Ï(x) is a given positive strictly increasing, twice continuously differentiable function on (0,â) such that Ï(0)â¥0. The goal is to maximize the probability criterion sup(μ,β)âM(x)P(yÏ=θÏ(xÏμ,β),Ïâ¤T0|x(0)=x,y(0)=y),x,yâDÏ, over a class of admissible controls M(x) consisting of bounded, Borel measurable functions. Under suitable conditions, it is shown that the maximal probability is given explicitly and the optimal process is determined explicitly by Ï(Ï(x),Ïâ²(x),Ïâ³(x))=μ0(x)Ïâ²(x)â(αâ12(Ïx+γ)2)Ï(x)β0(x)2.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Cloud Makasu,