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Estimating willingness-to-pay for a risk-averse person who can 'select' lotteries

I'm studying how the willingness-to-pay differs for individuals who can 'select' lotteries. Individuals are presented with L1 first and can pay some amount to get lottery L2. Assume these are my ...
comparing-lotteries-help's user avatar
1 vote
1 answer
94 views

Granger-Sims causality and subtle differences

For a bivariate process $(\textbf{X},\textbf{Y})=( (X_t, Y_t)^\top, t\in\mathbb{Z})$, we say that the process $\textbf{X}$ Sims-causes the process $\textbf{Y}$ (notation $\textbf{X}\overset{Sims}{\to}...
Albert Paradek's user avatar
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0 answers
27 views

transition probabilities from a AR(1) stochastic process

I have a stochastic volatility model for commodity price which follows an AR(1) process: ln(pt ) − m = ρ (ln(pt−1) − m) + exp(σt)ut ut ∼ IID(0, 1) σt − μ = ρσ(σt−1 − μ) + ηεt εt ∼ IID(0, 1) ...
Nusrat's user avatar
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2 votes
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126 views

Stochastic control of jumps of random size

Consider the problem of maximizing expected lifetime utility $$ V(a_t) \equiv \max_c\mathrm{E}_t \int_t^\infty e^{\rho (s - t)}u(c_t)\mathrm{d}t $$ subject to a state process $\mathrm{d}a_t$ which is ...
Wittgenstein's Poker's user avatar
1 vote
1 answer
54 views

Stochastic optimal control problem (calculus)

I am reading a paper with a stochastic optimal control problem. At one point the author faces the following Hamilton-Jacobi-Bellman (HJB) equation: $$\rho V(A)=\max_{c,w}\left\{ u(c)+V'(A)\left[(r(1-w)...
Alessandro's user avatar
2 votes
0 answers
47 views

Applications of a certain type of stochastic processes in macroeconomic, macroeconometric or finance

A compound Poisson random vector $Y$ is well defined in this site in wikipidia. Nothing prevents me from compound strictly stationary stochastic processes instead of compound random vectors. The ...
Letícia Fagundes's user avatar
3 votes
0 answers
64 views

Dynamic Information Provision model setup - It generalizes Dirk Bergemann and Stephen Morris

The following model setup is from the paper Dynamic Information Provision: Rewarding the Past and Guiding the Future by Ian Ball. It generalizes both the ideas of strategic information transmission of ...
Oliver Queen's user avatar
1 vote
0 answers
111 views

Market price of interest rate risk under the CIR model

My goal is to find the market price of risk associated with the interest rate under the CIR model whose stochastic differential equation under the physical measure is given: \begin{eqnarray}\label{...
user41162's user avatar
2 votes
1 answer
169 views

Bayes’ rule in "The sources of capital misallocation"

I am reading a paper titled "The sources of capital misallocation". In the model, firms are facing incomplete information about their future productivities. In particular, the productivity ...
Seyed Mahdi's user avatar
2 votes
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48 views

A conceptual question about the limitation of the MA processes

We know that linear time-series techniques are frequently used in macroeconometrics. The Wold Representation Theorem states that any covariance-stationary process may be expressed as an MA process ...
Fam's user avatar
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Derivation of autocovariances Lewis (2021) RES

I am studying this paper, and I don't understand the derivation of the covariances at the bottom of page 3090. Basically I have two shocks: $\varepsilon_{1t}$ has constant volatility $E[\varepsilon_{...
Giorgetto's user avatar
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2 votes
1 answer
40 views

Is playing against state of nature considered Stochastic game or Bayesian game?

Say if there is a team of gamblers betting on stock exchange. We can model the outcome of stock exchange as state of nature, because it is not deterministic. So the objective of team of gamblers is to ...
user0193's user avatar
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2 votes
1 answer
52 views

Bond Price expression

I've researching some mathematical finance and I've stumbled upon something I can't seems to find sources on. I'm probably overlooking something, but I hope someone can enlighten me and give me some ...
Marc Allan's user avatar
4 votes
0 answers
56 views

Value function iteration with stochastic productivity's standard deviation

Hello I would like to know how would you discretize the AR(1) process of technology in a standart RBC model when there is stochastic productivity's standard deviation. Namely I have: Technology $Z_t$ ...
BAL's user avatar
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4 votes
0 answers
78 views

Value function iteration with habit

I would like to know how I could write a value function when there are habits in preferences. I have the following equations: $$ u\left(C, t, H_{t}, L_{t}\right)=\frac{\left(C_{t} / H_{t}^{\kappa}\...
BAL's user avatar
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4 votes
1 answer
153 views

Stochastic AK model derivation

Consider the following version of the stochastic Ak model written as a Bellman equation: $$v(A,k)=max\ log(c)+\beta E[v(A',k')|A]$$ $$s.t\ k'+c\leq Ak$$ and non-negatitvities. $A$ is a stationary ...
Maybeline Lee's user avatar
1 vote
0 answers
35 views

Intuitive/Practical meaning of non-stationarity of GDP Data

As i just read in a time series book that a particular GDP data under consideration is non-stationary verified through various tests. From non-stationarity definition this means that the process has ...
pkg7724's user avatar
  • 11
1 vote
1 answer
455 views

Are overlapping generation (OLG) models extensions of a DSGE model?

Are overlapping generation models (OLG) extensions of a dynamic stochastic general equilibrium (DSGE) model? Or aren't these DSGE per se?
Beck Batucada's user avatar
1 vote
1 answer
61 views

Expectational stability: adaptive learning of RE equilibria in dynamic systems

There are two steps in the explanation of the expectational stability concept by Evans and Honkapohja (2001) (see below) that I don't understand. Step 1. What does this formula below mean, ...
Beck Batucada's user avatar
0 votes
1 answer
88 views

Limit of random walk auto correlation function

Given the random walk process $y_{t}=y_{t-1}+e_{t}$, the auto correlation function is given by $corr(y_{t}, y_{t-h})=(\frac{t-h}{t})^{1/2}=(1-\frac{h}{t})^{1/2}$, which tends to 0 as t tends to ...
Bob Charles's user avatar
0 votes
2 answers
1k views

Autocorrelation function of a random walk process

What is the intuition behind the result that the autocorrelation function of a random walk process $y_{t}=y_{t-1}+e_{t}$ tends to 1 as $t\rightarrow 0$? Thank you.
Bob Charles's user avatar
2 votes
1 answer
170 views

Purpose of Semidefinite Integral

I want to know the meaning of Semidefinite Integral. I am used to read definite and indefinite integral but I want to know the meaning of such equation : $\pi(e)\left(1-F\left[-\frac{a}{\pi(e)}\...
Alexandre's user avatar
-1 votes
1 answer
132 views

Stochastic process difference equation: stationary distribution

How can I find the stationary distribution (as t goes to infinity) of stochastic difference equations in the form: $x_{t+1} = a*x_t + b*N(0,1)$ where N(0,1) is a standard normal pdf I have ...
user14631's user avatar
1 vote
0 answers
135 views

Stochastic Dynamic Programming: Deriving the Steady-State for a Lottery

I am working through the basic examples of the stochastic RBC models in the book by McCandless (2008): The ABCs of RBCs, pp. 71 - 75 A Standard Stochastic Dynamic Programming Problem Here is a ...
Artem Kochnev's user avatar
3 votes
1 answer
120 views

Profit maximization under uncertainity

I have a seller say S and I have a buyer say B. Buyer’s willing to pay is equal to x which is private information. But Seller believe that it falls in the range [0,x1]. Seller’s belief distribution is ...
user avatar
1 vote
0 answers
53 views

Generalization of Tauchen 1986 approach to a case of time-varying volatility

My question is about generalization of Tauchen'86 approach to a case of time-varying volatility. Say, I have a process $$z_{t+1}=\rho z_t+\sigma_t \varepsilon_{t+1}$$ where $\varepsilon\sim \mathcal{...
vince's user avatar
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2 votes
0 answers
109 views

How to use Girsanov theorem to prove $\hat{W_t}$ is $\hat{\mathbb P}$-Brownian motion?

Assumptions: Let $T > 0$, and let $(\Omega, \mathscr F, \{\mathscr F_t\}_{t \in [0,T]}, \mathbb P)$ be a filtered probability space where $\mathbb P = \tilde{\mathbb P}$ (risk-neutral measure) and $...
BCLC's user avatar
  • 370
2 votes
1 answer
87 views

Given $\mathbb Q$ and $X_t$ is $\mathbb Q$-Brownian, find $\frac{d\mathbb Q}{d\mathbb P}$ / Uniqueness of Brownian or Radon-Nikodym derivative

The problem: Let $T >0$, and let $(\Omega, \mathscr F, \{ \mathscr F_t \}_{t \in [0,T]}, \mathbb P)$ be a filtered probability space where $\mathscr F_t = \mathscr F_t^W$ where $W = \{W_t\}_{t \in ...
BCLC's user avatar
  • 370
7 votes
2 answers
445 views

Application of Poisson process in economic modelling

To understand the emergence of constitution, Myerson (2008) models a scernario that a political leader gathers supports from captains in order to defeat challengers whose arrival is modelled by a ...
Metta World Peace's user avatar
8 votes
2 answers
2k views

Transition Matrix: Discrete -> Continuous Time

I have the code corresponding to Tauchen (1986) (Python equivalent of this), which generates a discrete approximation of a discrete time AR(1) process. For example, if you set up grid size as 3, it ...
FooBar's user avatar
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4 votes
1 answer
1k views

Proving there exists no arbitrage opportunities given 3 states and 2 assets

Assume there are 3 states of the world: w1, w2, and w3. Assume there are two assets: a risk-free asset returning Rf in each state, and a risky asset with Return R1 in state w1, R2 in state w2, and R3 ...
user2034's user avatar
  • 237
5 votes
2 answers
177 views

Find probability that payoff function is in $[10,20]$

In moment $t=0$ we bought option with expiration date $T=2$. The payoff function of this option is given by: $$f=(\max_{t\in[0,T]} S_t -110)^{+}$$ where $S_t$ satisfies $$dS_t=15dW_t$$ $$S_0=95$$ ...
luka5z's user avatar
  • 151
5 votes
2 answers
165 views

Decomposition of an additive functional into a Martingale part and other

This question relates to a theorem about the decomposition of additive functionals---a technique especially useful in macroeconomics and finance. This question has two objective. First, I don't have a ...
jmbejara's user avatar
  • 9,355
6 votes
1 answer
115 views

Showing that a transformation is measure preserving

Note: This question is related to this question about the construction of stochastic processes. Specifically, it relates to the transformation $\mathbb S: \Omega \rightarrow \Omega$ that is mentioned. ...
jmbejara's user avatar
  • 9,355
13 votes
3 answers
1k views

Understanding the construction of stochastic processes

I've seen stochastic processes modeled/constructed in the following way. Consider the probability space $(\Omega, \mathcal F, Pr)$ and let $\mathbb S$ be the (measurable) transformation $\...
jmbejara's user avatar
  • 9,355