Questions tagged [optimal-control]

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How do I use the Malliavin calculus to solve for the optimal trading strategy in the classic Merton problem?

How do I use the Malliavin calculus to solve for the optimal trading strategy in the classic Merton problem? In Duffie's book "Dynamic Asset Pricing," he outlines the "Martingale method" of solving ...
5
votes
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54 views

Optimization in discrete time

I have made optimizations in continuous time that belong to the control theory, for example one case: $\max(\min)V[u(t)]=\int_0^Tf(t,x(t),u(t))dt$ constraint to: $\dot x=g(t,x(t),u(t))$ Where: $x(t)$: ...
3
votes
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20 views

Deriving the Euler equation from a Continuous Time Dynamic Programming Problem (HJB)

Solving for the Euler equation in discrete time is farily straight forward with the use of the benveniste scheinkman theorem. However for the following standard ramsey model: $$max \int_{0}^{\infty}e^{...
3
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110 views

What are the boundary value conditions for generic HJBs in economics?

Consider a routine continuous time optimization problem: $ V(t,a_{t}) := \max \int_{\tau=t}^{\tau = T} e^{-\rho (\tau -t)} u(c_{\tau})d\tau $ $\text{ s.t. }$ $\dot{a}_{t} = y + ra_{t} - c_{t}$, $a_{...
3
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67 views

Converging Trajectories and Sufficiency for Optimality

(The question is loosely relatet to this thread.) In the paper "Feedback Equilibria for a class of non-linear Differential Games" by Mäler et al. it is stated (p. 14) In fact sufficiency is ...
2
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0answers
58 views

Finding optimal path in continuous time

I have the following optimal control problem $$\max_{c_t,l_t} \int_0^{\infty} [ln(c_t)+\theta ln(1-l_t)]e^{-pt}dt$$ st. $$\dot{k_t}=k_t^{1/2}l_t^{1/2}-c_t-\beta l_t$$ $$k_0>0$$ I do big part of ...
1
vote
0answers
39 views

Constancy of current value Hamiltonian and numeric computations

I am playing with a simple, continuous time optimal growth problem to learn optimal control. The social planner chooses $c_t$ to maximize: $$\int_0^\infty e^{-\rho t}u(c_t)dt$$ where $$\dot k_t=f(k_t)-...
1
vote
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54 views

discount factor on rival and non-rival goods

I am asking to myself if we must use a different discount rate on rival and non rival goods. In standard Solow-Swann model, we use generally the discount factor $\rho$. More formally, let's give the ...