- January 29th, 2015, 5:27 am
- Forum: Numerical Methods Forum
- Topic: Is HJB equation a local or global optimum?
- Replies:
**1** - Views:
**4622**

<r>I am a bit confused on the HJB equation. In the derivation of Hamilton?Jacobi?Bellman (HJB) equation, we take the first order optimality at each time step, so that the trading strategy is optimum over the next infinitesimal time step. It seems that this strategy gives only local optimum, which is...

- January 21st, 2015, 1:11 am
- Forum: Numerical Methods Forum
- Topic: How to calibrate stochastic model with time series?
- Replies:
**4** - Views:
**4730**

Thanks a lot, Alan

- January 20th, 2015, 1:34 am
- Forum: Numerical Methods Forum
- Topic: How to calibrate stochastic model with time series?
- Replies:
**4** - Views:
**4730**

<t>Thanks again, Alan. I want to use maximum likelihood, but I am not sure how to construct the likelihood function for specific stochastic models, especially high dimensional models. I think mathematica, matlab only provide optimizaiton functions, rather than likelihood function. Are there any good...

- January 19th, 2015, 1:23 am
- Forum: Numerical Methods Forum
- Topic: How to calibrate stochastic model with time series?
- Replies:
**4** - Views:
**4730**

<t>How to calibrate stochastic model with time series? I know there are lots of numerical methods like solving Fokker-Planck PDE, Disrete maximum likelihood, Hermite polynomial expansion, Markov Chain Monte Carlo. But is there any availble numerical library to do this? I prefer open source library. ...

- January 15th, 2015, 4:59 am
- Forum: Student Forum
- Topic: How to derive Hamilton-Jacobi-Bellman Equation from supreme of expectation?
- Replies:
**3** - Views:
**3216**

<t>Thank you, Alan. I know what you mean. I agree that Equation (2) can be derived from g(t, Vt, Xt)=sup[E( g(T, VT, XT) ) ].But I am still not sure how to get g(t, Vt, Xt) from Equation (1). There is an exponetial function and a parameter alpha in Equation (1), which finally disppear in Equaiton (2...

- January 14th, 2015, 9:32 am
- Forum: Student Forum
- Topic: How to derive Hamilton-Jacobi-Bellman Equation from supreme of expectation?
- Replies:
**3** - Views:
**3216**

- January 14th, 2015, 12:46 am
- Forum: Student Forum
- Topic: A quick question on Ito's integral
- Replies:
**8** - Views:
**3587**

Thank you Alan. I completely agree with you

- January 12th, 2015, 3:03 pm
- Forum: Student Forum
- Topic: A quick question on Ito's integral
- Replies:
**8** - Views:
**3587**

<t>The above solution uses a simple method to calculate It-Is.Although the result looks quite correct to me, the process seems to have some problem. The last equation omit lots of terms. After t1, there should be more terms t2, t3... until t. If we write out the long series (rather than just 3 terms...

- January 5th, 2015, 7:51 am
- Forum: General Forum
- Topic: How to forecast volatility based on fundamental analysis?
- Replies:
**1** - Views:
**3151**

<t>I know there are lots of papers and books cover forecasting volatility by quantitative model. However, is there any practical guide on forecast volatility based on fundamental analysis, like the analysis on government policy, economic conditions of foreign/domestic countries, customers' demand an...

- December 31st, 2014, 8:10 am
- Forum: Student Forum
- Topic: 2D martingale problem
- Replies:
**5** - Views:
**3450**

Thank you Alan. I have sth to pick up.

- December 29th, 2014, 1:32 am
- Forum: Student Forum
- Topic: 2D martingale problem
- Replies:
**5** - Views:
**3450**

Is there anything unclear on this question? The interviewer suggested a martingale be constructed in 2D to solve this problem, but I really cannot figure it out. Any further suggestions from you guys?

- December 27th, 2014, 9:30 am
- Forum: Student Forum
- Topic: 2D martingale problem
- Replies:
**5** - Views:
**3450**

<t>This is an interview question. Circle A with radius a is inside Circle B with radius b. a 2D independent Brownian motion start from point M with distance r to center of circle A. point M locates between circle A and cirlce B. What's the probability of reaching circle A before reaching circle B? <...

- December 24th, 2014, 12:11 am
- Forum: Numerical Methods Forum
- Topic: Why pricing American option by free-boundary method and MC?
- Replies:
**5** - Views:
**4546**

<t>Thank you, Cuchulainn.The finite difference scheme I use is Crank?Nicolson, which is second order accuracy. Do you mean assigning payoff to option price directly would make the accuracy order to 1? If so, can a classical 4th order Runge-Kutta can cure this disadvantage, where I can assign payoff ...

- December 23rd, 2014, 3:10 pm
- Forum: General Forum
- Topic: Expectation of volatility or sqrt(expectation of variance)?
- Replies:
**6** - Views:
**3669**

Thank you for your suggestions Alan.

- December 23rd, 2014, 3:07 pm
- Forum: Numerical Methods Forum
- Topic: Why pricing American option by free-boundary method and MC?
- Replies:
**5** - Views:
**4546**

<t>As I know, American-type option can be solved by PDE method. When the PDE is integrated backward, the option price can be simply assigned by option payoff at this time step if the payoff is bigger. This method seems work well for me, but is there any disadvantage of this method? Otherwise why do ...

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