Optimal strategy - HJB equation - Change to Mathematics
$begingroup$
I am sitting with the following control problem.
Given know the controlled Markov equation
begin{align}
dX_t&=-lambda X_tcdot dt+ U_tcdot dt+sigmasqrt{1+X_t^2}cdot dB_t
end{align}
with the performance objective function
begin{align}
mathbb{E}left[int_0^T left(frac{1}{2}qX_t^2+frac{1}{2}U_t^2right)dt +frac{1}{2}alphacdot X_T^2right]
end{align}
The goals is to minimize the performance function over all Markov controls $U_t=mu(X_t,t)$.
Furthermore, I want to determine a $alpha>0$ such that for all $q>0$, the optimal control does not depend on $t$, i.e. $U_t=mu(X_t)$.
Question: The question I have here is how to determine the $alpha>0$ such that for all $q>0$, $U_t=mu(X_t)$.
Does anybody have an idea?
stochastic-calculus sde hamilton-jacobi-equation
edited Dec 17 '18 at 14:04
LutzL
59k42056
asked Dec 17 '18 at 13:39
Jonathan KierschJonathan Kiersch
1089
$endgroup$
add a comment |
$begingroup$
I am sitting with the following control problem.
Given know the controlled Markov equation
begin{align}
dX_t&=-lambda X_tcdot dt+ U_tcdot dt+sigmasqrt{1+X_t^2}cdot dB_t
end{align}
with the performance objective function
begin{align}
mathbb{E}left[int_0^T left(frac{1}{2}qX_t^2+frac{1}{2}U_t^2right)dt +frac{1}{2}alphacdot X_T^2right]
end{align}
The goals is to minimize the performance function over all Markov controls $U_t=mu(X_t,t)$.
Furthermore, I want to determine a $alpha>0$ such that for all $q>0$, the optimal control does not depend on $t$, i.e. $U_t=mu(X_t)$.
Question: The question I have here is how to determine the $alpha>0$ such that for all $q>0$, $U_t=mu(X_t)$.
Does anybody have an idea?
stochastic-calculus sde hamilton-jacobi-equation
edited Dec 17 '18 at 14:04
LutzL
59k42056
asked Dec 17 '18 at 13:39
Jonathan KierschJonathan Kiersch
1089
$endgroup$
add a comment |
$begingroup$
I am sitting with the following control problem.
Given know the controlled Markov equation
begin{align}
dX_t&=-lambda X_tcdot dt+ U_tcdot dt+sigmasqrt{1+X_t^2}cdot dB_t
end{align}
with the performance objective function
begin{align}
mathbb{E}left[int_0^T left(frac{1}{2}qX_t^2+frac{1}{2}U_t^2right)dt +frac{1}{2}alphacdot X_T^2right]
end{align}
The goals is to minimize the performance function over all Markov controls $U_t=mu(X_t,t)$.
Furthermore, I want to determine a $alpha>0$ such that for all $q>0$, the optimal control does not depend on $t$, i.e. $U_t=mu(X_t)$.
Question: The question I have here is how to determine the $alpha>0$ such that for all $q>0$, $U_t=mu(X_t)$.
Does anybody have an idea?
stochastic-calculus sde hamilton-jacobi-equation
edited Dec 17 '18 at 14:04
LutzL
59k42056
asked Dec 17 '18 at 13:39
Jonathan KierschJonathan Kiersch
1089
$endgroup$
I am sitting with the following control problem.
Given know the controlled Markov equation
begin{align}
dX_t&=-lambda X_tcdot dt+ U_tcdot dt+sigmasqrt{1+X_t^2}cdot dB_t
end{align}
with the performance objective function
begin{align}
mathbb{E}left[int_0^T left(frac{1}{2}qX_t^2+frac{1}{2}U_t^2right)dt +frac{1}{2}alphacdot X_T^2right]
end{align}
The goals is to minimize the performance function over all Markov controls $U_t=mu(X_t,t)$.
Furthermore, I want to determine a $alpha>0$ such that for all $q>0$, the optimal control does not depend on $t$, i.e. $U_t=mu(X_t)$.
Question: The question I have here is how to determine the $alpha>0$ such that for all $q>0$, $U_t=mu(X_t)$.
Does anybody have an idea?
stochastic-calculus sde hamilton-jacobi-equation
stochastic-calculus sde hamilton-jacobi-equation
edited Dec 17 '18 at 14:04
LutzL
59k42056
asked Dec 17 '18 at 13:39
Jonathan KierschJonathan Kiersch
1089
edited Dec 17 '18 at 14:04
LutzL
59k42056
asked Dec 17 '18 at 13:39
Jonathan KierschJonathan Kiersch
1089
edited Dec 17 '18 at 14:04
LutzL
59k42056
edited Dec 17 '18 at 14:04
LutzL
59k42056
edited Dec 17 '18 at 14:04
LutzL
59k42056
59k42056
asked Dec 17 '18 at 13:39
Jonathan KierschJonathan Kiersch
1089
asked Dec 17 '18 at 13:39
Jonathan KierschJonathan Kiersch
1089
asked Dec 17 '18 at 13:39
Jonathan KierschJonathan Kiersch
1089
1089
add a comment |
add a comment |
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