{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:24:43Z","timestamp":1787322283187,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2002,1]]},"abstract":"<jats:p>In this paper, we define and study a new class of optimal stochastic control problems which is closely related to the theory of backward SDEs and forward-backward SDEs. The controlled process $(X^\\nu,Y^\\nu)$ takes values in ${\\mathbb R}^d \\times {\\mathbb R}$ and a given initial data for $X^{\\nu}(0)$. Then the control problem is to find the minimal initial data for $Y^{\\nu}$ so that it reaches a stochastic target at a specified terminal time T. The main application is from financial mathematics, in which the process $X^{\\nu}$ is related to stock price, $Y^{\\nu}$ is the wealth process, and $\\nu$ is the portfolio.<\/jats:p>\n                  <jats:p>We introduce a new dynamic programming principle and prove that the value function of the stochastic target problem is a discontinuous viscosity solution of the associated dynamic programming equation. The boundary conditions are also shown to solve a first order variational inequality in the discontinuous viscosity sense. This provides a unique characterization of the value function which is the minimal initial data for $Y^{\\nu}$.<\/jats:p>","DOI":"10.1137\/s0363012900378863","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"404-424","source":"Crossref","is-referenced-by-count":75,"title":["Stochastic Target Problems, Dynamic Programming, and Viscosity Solutions"],"prefix":"10.1137","volume":"41","author":[{"given":"H. 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