SERVING THE QUANTITATIVE FINANCE COMMUNITY

Search found 102 matches

  • 1
  • 2
  • 3
  • 4
  • 5
  • 7
by EdisonCruise
Yesterday, 1:17 am
Forum: General Forum
Topic: What’s Ito’s lemma for Poisson process in this function?
Replies: 5
Views: 404

Re: What’s Ito’s lemma for Poisson process in this function?

Thank you. I have corrected the typo. However, in \(dY_t=Z_{N_t} dN_t\), \(Z_{N_t}\) is a random variable, indicating the random jump size. I think it makes sense to include an expectation w.r.t.  \(Z_{N_t} \) in the drift term, as in page 26 of  http://people.ucalgary.ca/~aswish/JumpProcesses.pdf ...
by EdisonCruise
November 18th, 2019, 8:53 am
Forum: General Forum
Topic: What’s Ito’s lemma for Poisson process in this function?
Replies: 5
Views: 404

Re: What’s Ito’s lemma for Poisson process in this function?

Thank you Alan. May I ask one more question? In page 645 of your given file, there is an Ito formula for the compensated compund Poisson process: $$f(Y_t)=f(0)+\int_0^t \!(f(Y_s)-f(Y_s-))(dN_s-\lambda ds)+\lambda \int_0^t \!(f(Y_s)-f(Y_s-))ds$$ where \(dY_t=Z_{N_t} dN_t \) is a compound Poisson proc...
by EdisonCruise
November 16th, 2019, 10:25 am
Forum: General Forum
Topic: What’s Ito’s lemma for Poisson process in this function?
Replies: 5
Views: 404

What’s Ito’s lemma for Poisson process in this function?

If \(N_t\) is a Poisson process with intensity \(\lambda \),and \(dX_t=\delta dN_t\), \(q_t=-N_t\), then the Ito's lemma for function \(H(X_t)\) should be $$ dH(X_t)=[H(X_t+\delta)-H(X_t)]dN_t$$ For the function   \(H(X_t,q_t)\), why it is not something like this? $$ dH(X_t,q_t)=[H(X_t+\delta,q_t)-H...
by EdisonCruise
October 15th, 2019, 3:10 am
Forum: Technical Forum
Topic: Why is Bellman Equation solved by backwards?
Replies: 32
Views: 4572

Re: Why is Bellman Equation solved by backwards?

Thank you katastrofa. I think your explanation make sense.
by EdisonCruise
October 10th, 2019, 1:35 am
Forum: Technical Forum
Topic: Is there any stochastic control literature about a linear combination of variables?
Replies: 0
Views: 1494

Is there any stochastic control literature about a linear combination of variables?

Suppose I have a portfolio of N options and they are affected by M Brownian motions, where M<<N. I hope to maximize the expected return of this portfolio, which is a linear combination of each stock’s return. Then how to formulate the HJB equation? Is there any classical literature/material about th...
by EdisonCruise
July 24th, 2019, 2:33 am
Forum: Technical Forum
Topic: Why is Bellman Equation solved by backwards?
Replies: 32
Views: 4572

Re: Why is Bellman Equation solved by backwards?

Thank you Alan. I can understand the option pricing problem. The BS pde must be solved by backwards, only because the terminal condition, i.e., the option pay off, is well defined. The initial option price is unknown(or cannot be difined), so need to be solved. This is not because of the data is non...
by EdisonCruise
July 23rd, 2019, 1:13 am
Forum: Technical Forum
Topic: Why is Bellman Equation solved by backwards?
Replies: 32
Views: 4572

Re: Why is Bellman Equation solved by backwards?

Thank you all, but I what I cannot understand is the real reason that Bellman equation is ususally solved by backwards. Can any one give an exmaple in which both intitial and terminal conditions are well defined, but the Bellman equation can only be solved by backwards?
by EdisonCruise
July 22nd, 2019, 8:30 am
Forum: Technical Forum
Topic: Why is Bellman Equation solved by backwards?
Replies: 32
Views: 4572

Re: Why is Bellman Equation solved by backwards?

Thank you katstrofa. I aslo think the Bellman equation can be solve by forwards with well defined and NON-stationary data. But that's in contrast to Nicole Bäuerle and Ulrich Rieder' book. I cannot understand why the stationarity of data is related to forward/backward solution.
by EdisonCruise
July 22nd, 2019, 1:18 am
Forum: Technical Forum
Topic: Why is Bellman Equation solved by backwards?
Replies: 32
Views: 4572

Re: Why is Bellman Equation solved by backwards?

I cannot make a specific example, because I read that in a book. The followingsa are the images I took from Nicole Bäuerle and Ulrich Rieder' book. Maybe I can rephase the question, if the initial condition is well defined and the data is NON-stationary, can the Bellman equation be solved by forward...
by EdisonCruise
July 21st, 2019, 3:13 pm
Forum: Technical Forum
Topic: Why is Bellman Equation solved by backwards?
Replies: 32
Views: 4572

Why is Bellman Equation solved by backwards?

I though Bellman Equation was solved by backwards because the terminal condition is easier to define than the initial condition. Until recently, I read the book Markov decision processes with application to finance by Nicole Bäuerle and Ulrich Rieder. It says ‘Due to the stationarity of the data ho...
by EdisonCruise
June 1st, 2019, 10:21 am
Forum: Brainteaser Forum
Topic: What's the optimal strategy to this food transportation problem?
Replies: 3
Views: 2281

What's the optimal strategy to this food transportation problem?

The distance between city A and B  is 100 km. The total food needs to move from A to B is 3 tons. A transportation team can carry food 1 ton per day and at the same time consumes food 0.25 tons per day. Then how to setup transfer stations between city A nd B to minimize food consumption during tran...
by EdisonCruise
May 29th, 2019, 12:34 am
Forum: Numerical Methods Forum
Topic: How to calibrate an exponential distribution with scale?
Replies: 6
Views: 2244

Re: How to calibrate an exponential distribution with scale?

I think the model should work for small-tick-size assets. But for most of other asset types, this model is not applicable directly.
by EdisonCruise
May 28th, 2019, 1:32 am
Forum: Numerical Methods Forum
Topic: How to calibrate an exponential distribution with scale?
Replies: 6
Views: 2244

Re: How to calibrate an exponential distribution with scale?

Thank you for your reminding. I confused something here. \(\lambda(\delta)=Aexp(-\kappa\delta) \) is not a pdf. This  model  is from the paper "High-frequency trading in a limit order book "by MARCO AVELLANEDA and SASHA STOIKOV.  \(\lambda(\delta)=Aexp(-\kappa\delta) \) is acutally the exponential a...
by EdisonCruise
May 27th, 2019, 3:46 am
Forum: Numerical Methods Forum
Topic: How to calibrate an exponential distribution with scale?
Replies: 6
Views: 2244

How to calibrate an exponential distribution with scale?

I want to fit an exponential arrival rate from my data with below model, a more detail is given in my next post: $$\lambda(\delta)=Aexp(-\kappa\delta) $$ MATLAB can fit an exponential distribution with the following pdf: $$Y(\delta)=\frac{1}\mu exp(-\frac{\delta}\mu) $$ But is there any way to conve...
by EdisonCruise
May 7th, 2019, 2:12 am
Forum: Numerical Methods Forum
Topic: Why the minimum is taken here when its derivative > 0?
Replies: 2
Views: 2103

Why the minimum is taken here when its derivative > 0?

Below are sentensce taken from a paper. "In fact, we are going to prove that $$\forall t\in[0,T],\forall q\in\{-Q,...,Q\},\nu_q(t)\ge e^{-(\alpha Q^2-\eta)(T-t)} $$ If this was not true then there would exist \(\epsilon \gt0\) such that: $$\min_{t,q}e^{-2\eta(T-t)}(v_q(t)-e^{-(\alpha*Q^2-\eta)(T-t)}...
  • 1
  • 2
  • 3
  • 4
  • 5
  • 7
GZIP: On