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by EdisonCruise
July 24th, 2019, 2:33 am
Forum: Technical Forum
Topic: Why is Bellman Equation solved by backwards?
Replies: 14
Views: 835

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: 14
Views: 835

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: 14
Views: 835

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: 14
Views: 835

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: 14
Views: 835

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: 543

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: 555

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: 555

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: 555

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: 471

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)}...
by EdisonCruise
January 15th, 2018, 6:37 am
Forum: Numerical Methods Forum
Topic: What makes autoregression different from multiple linear regression?
Replies: 2
Views: 945

Re: What makes autoregression different from multiple linear regression?

Thank you Alan. But when I use matlab to estimate its VAR model, besides the coefficients in the linear equations, matlab also estimates the covariance matrix as unknowns. In multiple linear regression, there is no covariance matrix or autocorrelation to estimate, because samples are assumed to be i...
by EdisonCruise
January 10th, 2018, 4:12 pm
Forum: Numerical Methods Forum
Topic: What makes autoregression different from multiple linear regression?
Replies: 2
Views: 945

What makes autoregression different from multiple linear regression?

For an AR(2) process Yt=a1*Yt-1+a2*Yt-2+b, is it different from Y=a1*X1+a2*X2+b, where X1 and X2 can be replaced by Yt-1 and Yt-2 respectively? As I know, the estimation of both models can use least square method and some book state’ We can therefore state that in the case of VAR processes, the LS e...
by EdisonCruise
May 24th, 2017, 8:33 am
Forum: Trading Forum
Topic: How to trade open price in practice as in my backtest?
Replies: 10
Views: 1119

Re: How to trade open price in practice as in my backtest?

Thank you. I am new in this area. Do you have any recommeded paper or book on this topic? 
by EdisonCruise
May 23rd, 2017, 9:40 am
Forum: Trading Forum
Topic: How to trade open price in practice as in my backtest?
Replies: 10
Views: 1119

Re: How to trade open price in practice as in my backtest?

Thank you all for your replies. My strategy is that first to forecast the up or down of a stock in the coming 5 days. If up, I buy, otherwise short. After 5 days, I close my position. In my back test, I just use the open price to open and close my position. 5 days should be a relatively long period....
by EdisonCruise
May 22nd, 2017, 6:43 am
Forum: Trading Forum
Topic: How to trade open price in practice as in my backtest?
Replies: 10
Views: 1119

Re: How to trade open price in practice as in my backtest?

Thank you. But which price should I use in back test? Should I use the first 5 minute price averaged by volume?
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