9

I am the last person that should be answering continuous time questions like these, but if there's no one else I guess I'll give it a shot. (Any correction of my dimly remembered continuous-time finance is very welcome.) My impression has always been that this is best interpreted as a consequence of the martingale representation theorem. First, though, I'll ...


5

Equilibria: in the macroeconomic sense of aggregate equilibrium where all markets clear, markets are most likely never in any equilibrium but rather in constant flux between different equilibria, because the market clearing macroeconomic equilibrium always depends on real and also in short run nominal factors which constantly change. Hence it does not make ...


5

Complete market is a market where every possible asset or good can be assigned a price and where you have perfect information, can make perfect contracts and zero transaction costs. Any market can be complete regardless of its market structure. So you can have complete market dominated by monopoly, or oligopoly or monopolistic competition etc. Perfectly ...


5

I've been meaning to post this for a long time. I came across this and thought it could add some insight. This example is from "Financial Asset Pricing Theory" by Munk. Consider the following figure. How many assets do we need to have a complete market? You might think that, because there are 6 different states here, we need at least 6 different ...


2

Here is a simple fact: In your notation, the model under consideration is complete if and only if the matrix \begin{bmatrix} 1+R & 1+R \\ d & u \end{bmatrix} is one-to-one, i.e. $d \neq u$. (Equivalently, its transpose is onto, which is what is shown in your quoted text.) No-arbitrage holds if and only if $d \leq 1+R \leq u$ and $d < u$. (By ...


2

From a Wikipedia page linked to in the question: [emphasis by me] Examples of games with incomplete but perfect information are conceptually more difficult to imagine, such as a Bayesian game. The board game Ticket to Ride is one example, where players' resources and moves are known to all, but their objectives (which routes they seek to complete) are ...


2

You are right, it is the same thing. Actually, later on the book the density over the history $s^t = [s_t, s_{t-1}, \cdots, s_0]$ is written as $$ \pi(s^t) = \pi(s_t|s_{t-1}) \cdots \pi (s_1|s_0)\pi(s_0) \tag{2.3.1} $$ where $\pi(s_0)$ denotes the probability of the initial state (or $\pi_0(s_0)$ if you wish), and $\pi(s|s')$ is a transition probability. ...


1

Since this is a Markov chain \begin{eqnarray} \pi_t(0,0,\cdots,1,1) &=& \color{blue}{\pi(s_t = 0 | s_{t - 1} = 0)} \cdots \color{magenta}{\pi(s_2 = 0 | s_{1} = 1)} \color{red}{\pi(s_1 = 1 | s_{0} = 1)}\color{orange}{\pi(s_0 = 1)} \\ &=& \color{blue}{1} \times \cdots\times \color{magenta}{0.5}\times\color{red}{1}\times \color{orange}{1} = 0....


1

It depends on what you want from a representative agent. What you get is a representative agent at the given prices. For any two commodities, you have relative prices. This is where market completeness comes in. All you have to do now is find a well-behaved utility function whose marginal rate of substitution between the commodities corresponds to the ...


1

I guess it just follows by definition. Assume that in the high state (for household $i$, aggregate endowment is 10, and household $i$ consumes $1/5 = 2$ of this, while having an endowment of $5$. Now consider what happens if we were in the low state (for household $i$), where household $i$ only gets $1$ of whatever endowment. However, if this is a high ...


1

Thanks a lot for the reference. I think the result does hold. Here is what I found: The validity of such a law of large numbers what subject to some debate in the 1980s. See Judd (1985), Feldman and Gilles (1985) and Uhlig (1996) for representative papers. Luckily Feldman and Gilles show that for a probability space $(Y; B(Y ); \Pi)$ there exists a ...


Only top voted, non community-wiki answers of a minimum length are eligible