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
0answers
65 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: $x(t)$: ...
4
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0answers
60 views

Solve the Ben-Porath Model (Optimal Control Problem)

Suppose we have a Ben-Porath style human capital investment model, in which the representative agent maximize her lifetime earnings: $$V(h, a)=\max \int_{a}^{R} e^{-r(t-a)}\left[ w h(t)(1-n(t))-px(t)\...
3
votes
0answers
126 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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0answers
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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60 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
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41 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
0answers
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 ...
0
votes
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21 views

Why isn't the Federal Reserve interest rate set by a published algorithm?

The Federal Reserve sets the interest rate, presumably based on a number characteristics and trends in the economy: inflation, GDP growth, population growth, unemployment, housing prices, etc. However,...