TY - GEN
T1 - A risk-averse analog of the Hamilton-Jacobi-Bellman equation
AU - Ruszczyński, Andrzej
AU - Yao, Jianing
PY - 2015
Y1 - 2015
N2 - In this paper, we study the risk-averse control problem for diffusion processes. We make use of a forward-backward system of stochastic differential equations to evaluate a fixed policy and to formulate the optimal control problem. Weak formulation is established to facilitate the derivation of the risk-averse dynamic programming equation. We prove that the value function of the risk-averse control problem is a viscosity solution of a risk-averse analog of the Hamilton-Jacobi-Bellman equation. On the other hand, a verification theorem is proved when the classical solution of the equation exists.
AB - In this paper, we study the risk-averse control problem for diffusion processes. We make use of a forward-backward system of stochastic differential equations to evaluate a fixed policy and to formulate the optimal control problem. Weak formulation is established to facilitate the derivation of the risk-averse dynamic programming equation. We prove that the value function of the risk-averse control problem is a viscosity solution of a risk-averse analog of the Hamilton-Jacobi-Bellman equation. On the other hand, a verification theorem is proved when the classical solution of the equation exists.
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U2 - 10.1137/1.9781611974072.63
DO - 10.1137/1.9781611974072.63
M3 - Conference contribution
AN - SCOPUS:84961954160
T3 - SIAM Conference on Control and Its Applications 2015
SP - 462
EP - 468
BT - SIAM Conference on Control and Its Applications 2015
A2 - Bonnet, Catherine
A2 - Ozbay, Hitay
A2 - Pasik-Duncan, Bozenna
A2 - Zhang, Qing
PB - Society for Industrial and Applied Mathematics Publications
T2 - SIAM Conference on Control and Its Applications 2015
Y2 - 8 July 2015 through 10 July 2015
ER -