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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 ...
jmbejara's user avatar
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15 votes
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1k views

How do I compute the relative risk aversion of Epstein-Zin preferences?

$$ \newcommand{\E}{\mathbb{E}} $$ Preface This question is related to this one about the elasticity of intertemporal substitution and this one about the definition of absolute risk aversion. (It's ...
jmbejara's user avatar
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13 votes
0 answers
895 views

Modern theory of integrability of demand?

I am aware of Hurwickz Uzawa work in integability, neatly summarized by Border http://people.hss.caltech.edu/~kcb/Notes/Demand4-Integrability.pdf I am wondering if there is any modern treatment of the ...
user157623's user avatar
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13 votes
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490 views

Can I refine the set of equilibria in a signaling game to the sender-optimal outcome?

Main question: I've been reading about communication games a lot, and I'm wondering if there are good criteria to select between two separating-ish equilibria. I think of a separating equilibria as ...
Pburg's user avatar
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12 votes
0 answers
339 views

Proofs in the Appendix A of Sannikov (2007)

I have a few questions about the proofs in Appendix A of Sannikov (2007), Games with Imperfectly Observable Actions in Continuous Time. In lemma 4, when he shows the Lipschitz continuity of $H_a(w,\...
Theoretical Economist's user avatar
12 votes
0 answers
172 views

Queuing Discipline and Lipschitz Continuity

I was reading a paper by Platz and Østerdal (2014) titled "The curse of the first-in-first-out queue discipline". I was wondering about a particular section of it, particularly the part about last-in-...
Kitsune Cavalry's user avatar
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12 votes
0 answers
501 views

How can I test for autoregressive residual terms in a fixed effects panel Poisson model?

I have panel data for counts of new firms in different regions for six years. I am estimating a static poisson regression with multiplicative fixed effects$^*$; I have also tried to estimate a dynamic ...
Matthijs's user avatar
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10 votes
0 answers
142 views

Replicating a state-space model

I am trying to replicate the results of Cochrane, 1998. Most of the paper is just describing the theory behind The Fiscal Theory of the Price Level. But from p. 42 he begins the econometrics aspect. ...
WoodfordJr's user avatar
9 votes
0 answers
142 views

Why aren't there more super-stars in educational content delivery?

The super-star phenomena seems to happen in any field where the marginal cost of distribution is very low. I think teaching could be that way just as much as acting or playing basketball - at least as ...
user avatar
8 votes
1 answer
143 views

Lab experiments of labour markets

I have been searching for papers that conduct lab experiments simulating a labour market, that means for a minimum there are both participants taking the role of firms, and participants taking the ...
Papayapap's user avatar
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7 votes
0 answers
160 views

Is 2SLS asymptotically MLE?

$$y_i =\beta_0 +\beta_1 x_{1i}+\beta_2 x_{2i}+\varepsilon_i$$ Suppose $x_1$ is endogenous but $x_2$ is exogenous. We have two excluded instruments, $z_1$ and $z_2$. The first stage is: $$x_{1i} =\...
Michael Gmeiner's user avatar
7 votes
0 answers
147 views

Small Open Economy Without Government

Suppose we have an economy with a representative consumer with the following utility function: $$U=\sum_{t=0}^\infty\beta^t\frac{c_t^{1-\sigma}}{1-\sigma} $$ There is no uncertainty and the household ...
Maybeline Lee's user avatar
7 votes
0 answers
255 views

Fixes of quadratic utility when probability of decreasing utility is large

In finance and specifically portfolio theory, a popular utility function is quadratic utility $$ u(x)=x-\frac{\lambda}{2}(x-\mu_x)^2 $$ where $x$ is wealth and $\lambda$ is the parameter of risk ...
Richard Hardy's user avatar
7 votes
1 answer
137 views

Auction mechanism with no trusted third-party

I have been using a double-auction mechanism to solve a two-sided market where multiple agents are competing to supply/use slices of a shared resource. The owner of the resource is a trustable third-...
Nima Afraz's user avatar
7 votes
0 answers
406 views

Dynamic Bertrand competition when players take turns

Consider the following game: There are two players, $i\in\{1,2\}$ Time is discrete and runs to infinity during periods $t=\{1,2,\ldots\}$ At eat point in time, players have a price $p_i(t)\in\mathbb{...
Ubiquitous's user avatar
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7 votes
0 answers
270 views

Has any progress been made on the Pacman Conjecture on Finite Time Horizons?

The Pacman conjecture states that the optimal strategy for monopolistic durable goods manufacturers is to set price high and slowly drop it (i.e. eating their way down the demand curve). Empirically ...
Jason Nichols's user avatar
6 votes
0 answers
141 views

Biggest breakthroughs in Economics in 2023

I recently went through a few videos by Quanta magazine, talking about what, in their opinion at least, are the biggest breakthroughs in Mathematics, Computer Science, Physics and Biology/ ...
Ishan Kashyap Hazarika's user avatar
6 votes
0 answers
113 views

Solving Rational Expectation Models Linear vs. Nonlinear

Since I am coding some linear New Keynesian models in python and solving them under rational expectations (using the method of undetermined coefficients/linear time iteration), I was wondering whether ...
Suttungr's user avatar
6 votes
0 answers
42 views

Do Human Resources use information on applicants' child rearing effort as a signal

In Spence's Job Market Signaling paper (a non-paywalled version is available here) firms observe applicants' educational investment. From these signals the firms glean information on the "type&...
Giskard's user avatar
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6 votes
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7k views

Topological intuition to continuous preference relation

For a Microeconomics Course, we are going through MWG, and in the lecture we discussed the notion of a continuous preference relation. A preference relation $\succsim$ on a set $X$ is called ...
J. Dekker's user avatar
6 votes
0 answers
883 views

Which is a better intermediate micro textbook: Perloff (with calculus) or baby Varian (with calculus)?

I’m currently learning intermediate microeconomics with calculus. I know to take derivatives, partial derivatives, integrals, and multiple integrals, and I know some basic linear algebra (solving ...
Tejas Subramaniam's user avatar
6 votes
1 answer
142 views

Signalling Model (Rearranging the FOCs of UMP)

I'm currently reading "SAVING RATES AND POVERTY: THE ROLE OF CONSPICUOUS CONSUMPTION AND HUMAN CAPITAL" by Omer Moav and Zvika Neeman, and I encounter some problem deriving one of the equations. ...
Estee L's user avatar
  • 61
6 votes
0 answers
117 views

How do you strategically vote to put someone in last place?

I watch a dumb reality TV show which has a certain number of contestants to start with, and every week one contestant is eliminated. Here's how the elimination process works. Every week a certain ...
Keshav Srinivasan's user avatar
6 votes
0 answers
31 views

Why do co-ops dominate in certain markets rather than more-conventional enterprises?

Why do co-ops dominate in certain markets rather than more-conventional enterprises? For example, the US dairy processing market seems to be dominated co-ops like Land'O Lakes and Dairy Farmers of ...
user809695's user avatar
5 votes
0 answers
75 views

p-hacking vs. parameter calibration?

I'm currently tasked in my job to design a Prospect Theory (here CPT-)index as mentioned in Barberis, Mukherjee and Wang (2016): "Prospect Theory and Stock Returns: An Empirical Test", see ...
T123's user avatar
  • 303
5 votes
0 answers
112 views

What are good analogies for explaining negative externalities?

I'm making an infographic about the negative externalities of driving, and I want to explain that taxation is not "just" a tool to get a desired effect; it's a price-correcting mechanism ...
Victor Nielsen's user avatar
5 votes
0 answers
110 views

Optimal level of consumption in discrete time model with quadratic preferences and infinite horizon

I am trying to derive an expression for the optimal level of consumption in the basic problem: $ max \hspace{1cm} U_t = E_t \left[\sum_{s=t}^{\infty} \beta^{s-t} \left( C_s - a\frac{Cs}{2}^2 \right) ...
Giorgetto's user avatar
  • 223
5 votes
0 answers
47 views

Comparing voting methods when there are only two voters

Consider the Schulze, Kemeny-Young, Ranked Pairs and Borda count voting methods. (The last is obviously the odd one out in this list!) Suppose that there are only two voters. Each voter gives a ...
cfp's user avatar
  • 252
5 votes
0 answers
52 views

Controversy surrounding the Fiscal Theory of the Price Level (FTPL)

I recently started reading a draft of John Cochrane's book on the Fiscal Theory of the Price Level. In the preface he states that the "[...] theoretical controversies are over." However, ...
Joe's user avatar
  • 185
5 votes
0 answers
77 views

In experiments of 2-by-2 games where the dominant action benefits both players, do people frequently choose the other action?

Sayers et al look in Some descriptive aspects of two-person non-zero-sum games at variations of the prisoner dilemma. They had two participants (α and β) pressing press either a black (1) or a red (2) ...
Christian's user avatar
  • 151
5 votes
0 answers
138 views

How to find an optimal strategy in an auction?

I have asked this question in mathematics forum as well but since I have not recieved an appropriate answer yet, I ask it here as well. Consider an auction of sculptures by four artists: A, B, C and D....
plpm's user avatar
  • 151
5 votes
0 answers
54 views

In the BLP paper, why interacting consumer characteristic with product characteristic can generate more desirable substitution pattern

Got a question about the famous BLP paper (http://people.stern.nyu.edu/wgreene/Econometrics/BLP.pdf). When there is no interaction between product characteristic and consumer characteristic, the ...
ExcitedSnail's user avatar
5 votes
0 answers
277 views

Constant returns to scale and cost function: $C(p,ty) = tC(p,y)$

How can I prove that for a production function $F:\mathbb X \rightarrow \mathbb R$ with constant returns to scale $$\forall x\in \mathbb X, \forall t > 0: \ \ F(tx) = t F(x)$$ and with the cost ...
user270396's user avatar
5 votes
0 answers
138 views

Certainty equivalence when the utility is semi-continuous instead of continuous

Let $U:\mathbb R^2\to\mathbb R$ be a utility function. If $U$ is strictly increasing and continuous, then it is well known that for any $(x_1,x_2)$ there exists a certainty $(c,c)$ such that $$U(x_1,...
High GPA's user avatar
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5 votes
0 answers
163 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: $x(t)$: ...
manifold's user avatar
  • 843
5 votes
0 answers
114 views

Parsing problem 1.D.5 in MWG

I am a little confused about the statement of 1.D.5 in MWG, which I will reproduce here for convenience. I have "solved" the problem, I just don't understand something particular. $\textbf{(...
Seh-kai 's user avatar
5 votes
0 answers
18 views

Datasets with pre- and post migration earnings

I am interested in computing the pre- and post-migration earnings of international migrants, especially those migrating from low income to high income countries (or vice versa). The data should allow ...
LutzHendricks's user avatar
5 votes
0 answers
50 views

Which classical liberal economists promoted the privacy and secrecy of businesses?

Quinn Slobodian (2018) writes: the idea of businessmen opening their account books beyond the firm represented a revision of the classical liberal vision. The privacy of the businessman was no ...
user avatar
5 votes
0 answers
231 views

Question about MWG 17.D.1

I tried to solve by myself the exercises of MWG(Mas Colell). However, I think the exercise has an error at 17.D.1. The 17.D.1 asks us that "verify that there are multiple equilibria". However, The ...
martian03's user avatar
  • 245
5 votes
0 answers
74 views

Estimates of magnitude of externalities generated by education?

It is standard to claim that education generates positive externalities. For example, Mankiw (2017, Principles of Economics, p. 193): education also yields positive externalities. One externality ...
user avatar
5 votes
0 answers
707 views

Public Bads and Non-Excludability

The term "public bad" is sometimes used for "goods" which, like public goods, are non-excludable and non-rival, but which tend to lower rather than raise welfare. Air pollution is an example. For a ...
Adam Bailey's user avatar
  • 8,519
5 votes
0 answers
135 views

Afriat theorem for negative goods

GARP and Afrait theorem assume that the alternative $x\in\mathbb R_+$ is always positive. In some economic contexts, such as financial choices, the attribute can be negative. I wonder if we can ...
High GPA's user avatar
  • 1,916
5 votes
0 answers
196 views

How to interpret the proof that information cascades will form?

I am reading the 1992 paper of Bikchandani, Hirshleifer and Welch on information cascades. They claim and prove that, given an environment of sequential decision making, an information cascade will ...
Rega Sota's user avatar
5 votes
0 answers
241 views

Solution to Dynamic Programming (Bellman Equation) Problem

Could someone please provide pointers on how to solve the below? If any theoretical approximations are possible, that would be very helpful. If numerical solutions are the right approach, could you ...
user249613's user avatar
5 votes
0 answers
66 views

Estimating Job Vacancy rate empirically

I'm currently reading up on matching models in terms of their ability to describe frictional unemployment, they generally follow a cobb-douglas form. $$M(u,v)=m=\mu u^\alpha v^{1-\alpha}$$ Where $M(...
EconJohn's user avatar
  • 8,405
5 votes
0 answers
55 views

Letting clients/guest reserve their space vs keeping space clear so that it is available for people who really need it at the moment

Everybody knows that moment when you are in search for a beach lounger but everything is covered by towels, yet the people who placed them there are untraceable, often back at the hotel or in the town ...
Johannes Ebster's user avatar
5 votes
0 answers
760 views

Fact-checking Dan Ariely (2008) on Duke basketball tickets story

In Predictably Irrational (2008, pp. 127-133), Dan Ariely describes the Krzyzewskiville phenomenon (Duke students camp for weeks to get basketball tickets), and how he and Ziv Camron used it to study ...
user avatar
5 votes
0 answers
222 views

Optimal Fight Purse and Boxing Strategies

The following is all public information available to all the players in this scenario. The General Setup In the aftermath of the infamous race between the tortoise and the hare, the salty hare went ...
Kitsune Cavalry's user avatar
  • 6,638
5 votes
0 answers
330 views

Why are inventions inevitably correlated with imperfect competition?

Romer (1990) elaborates the incompatibility of nonrival inputs with constant returns to scale: If a production function depends on rival and nonrival inputs and both inputs are productive, then the ...
Fusscreme's user avatar
  • 287
5 votes
0 answers
360 views

On the uniqueness of utility functions for both risk and time

I have a question regarding the uniqueness of preference functionals under risky and dynamic settings. Two well known models to represent preferences for both settings are the Expected Utility Model ...
thekiciminister's user avatar

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