Questions tagged [continuous-time]

The tag has no usage guidance.

26 questions
Filter by
Sorted by
Tagged with
1k views

Complete Markets in Continuous Time

In the standard discrete time economies with a finite number of states, $n$, a complete markets economy is simply an economy with $n$ independent assets (Think Ljunqvist and Sargent Chapter 8). This ...
493 views

Stochastic growth in continuous time

Literature: See Chang (1988) for theoretical part and Achdou et al. (2015) for numerical part respectively. Model Consider the following stochastic optimal growth problem in per capita notation. \...
1k views

References to learn continuous-time dynamic programming

Does anyone know of good references to learn continuous-time dynamic programming? The references don't have to be books. They could be links to online resources as well. Links to clear, concise ...
273 views

48 views

Relationship of continuous and discrete time models

I am trying to understand two comments from a colleague. I have no clue about continuous time models. He said something like "just replace $\delta$ with $e^{-rdt}$ the Poisson process becomes a ...
69 views

Matching problem in continuous time

Let's split each period into $n$ intervals. There's a continuum $u$ of unemployed and $v$ of vacancies. During each interval, there is a total of $X/n$ job offers. That means that each unemployed gets ...
186 views

371 views

165 views

Kolmogorov-Forward-Equation with Entry and Exit

I'll try to ask this question in the most simplistic environment possible, so lets think about a household that can consume and save. After some cumbersome work, we have solved for the optimal savings ...
61 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 ...
373 views

Solow model, time and steady state

Suppose we have a Solow model: $$Y(t)=C(t)+I(t)$$ $$I(t)=sY(t)$$ $$\dot K=I(t)-δK(t)$$ With a given Cobb-Douglas: $$Y(t)=Z(t)K^aL^{1-a}$$ $$y(t)=Y(t)/L(t)$$ $$k(t)=K(t)/L(t)$$  y=...
67 views

Computing the continuous time survival rate

We have a population of people with different age $a$, time is indexed with $t$. There is a rate at which people die, $d(a, t)$. For simplicity, ignore births. I want to compute the evolution of the ...
21 views

Continuous trading economies. I see this expression in many papers but I do not know what it means in the precise technical sense. And I'm not an economist. Maybe it could refer to an economic ...
46 views

Forward-Looking HJB: Rewrite as PDV

We live in continuous time. Let there be some discount rate $D(t)$, which consists of a discount rate, and some death probability. $V(t)$ contains the flow value of, say, being alive. If you are alive,...