To learn more, see our tips on writing great answers. “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…, Continuous-time, non-recursive ARIMA Equation, Reference Request for Fractional Brownian motion, Solution Geometric Brownian Brownian motion with no drift. This looks right to me, but maybe someone will have more to say! Finally, if the integrator is some stock price process $S_t$ instead of $W_t$, and $f(Y_t)$ is the number of stocks held (could be simply a constant, deterministic quantity), then I interpret the Ito Integral as the profit or loss of that stock portfolio over time. Can the President of the United States pardon proactively? Privacy What LEGO piece is this arc with ball joint? Identify the states of matter where Brownian Motion can occur. Question: 3. Brownian motion can take on negative values, so log of a Brownian motion is not a well defined quantity, I am not sure how to interpret it. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. What LEGO piece is this arc with ball joint? Why does chrome need access to Bluetooth? 1. What was the most critical supporting software for COBOL on IBM mainframes? MathJax reference. Looking for instructions for Nanoblock Synthesizer (NBC_038). These Brownian increments are at the same time the gambling game pay-off (so the game pays the bettor's bet multiplied by the next Brownian increment realization). I like to interpret Ito Integral as the outcome of a gambling strategy. quant.stackexchange.com/questions/58923/…, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…, “Question closed” notifications experiment results and graduation, Anticipating stochastic integral $\int_0^T W_T dW_t$, Ito Integral of functions of Brownian motion. CIE IGCSE Chemistry exam revision with questions and model answers for Diffusion, Brownian Motion, Solids, Liquids, Gases Multiple Choice 2. a) Diffusion. answer choices . 3. Why is Soulknife's second attack not Two-Weapon Fighting? Then a discrete Stochastic integral (finite sum, strictly speaking not an Ito integral) could be defined as: $I_{t=10}=\sum_{h=0}^{9}2\left(X_{h+1}-X_h\right)$. Q. In general, Ito Integral can be written as: $$I_t:=\int_{h=0}^{h=t}f(Y_h)dX_h=\lim_{n \to\infty}\sum_{h=0}^{n-1}f(Y_h)\left(X_{h+1}-X_h\right)$$. SURVEY . $X_h\epsilon${$-1,1$} with probability $0.5$), $Y_h=1$ and $f()=2$. Diffusion, Brownian Motion, Solids, Liquids, Gases Multiple Choice 1 | Model Answers Melody 2020-05-16T08:04:00+01:00 the betting game pays the realized Brownian $W_t$ at each moment in time multiplied by the bettor's bet corresponding to the last observed realization of $W_t$. Or asked another way, is there an $ARIMA(p,d,q)$ model that "corresponds to" geometric Brownian motion? Shouldn't some stars behave as black hole? 3. Did Star Trek ever tackle slavery as a theme in one of its episodes? In continuous time, the bettor constantly adjusts his or her bet to the "current" level of the Brownian motion $W_t$, which acts as the integrator: i.e. © 2003-2020 Chegg Inc. All rights reserved. answer choices . $f()$ is some well-behaved function that still makes $f(Y_t)$ square integrable. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Was the theory of special relativity sparked by a dream about cows being electrocuted? The reason for asking is $W_T$ can take negative values, so wanted to see the context. 20 Questions Show answers. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. I interpret the integrator $X_t$ as the outcome of the gambling game, whilst the integrand $f(Y_t)$ is the betting strategy. To learn more, see our tips on writing great answers. Question 1 . answer choices . What if the P-Value is less than 0.05, but the test statistic is also less than the critical value? If $W_t$ is standard Brownian motion, what is $\int_0^T W_t \ln(W_t) dW_t$? a) Diffusion. What if the P-Value is less than 0.05, but the test statistic is also less than the critical value? These integrals have a very clear math definition and sometimes appear in option pricing. What is the cost of health care in the US? Thanks for contributing an answer to Cross Validated! 1. 10 Questions Show answers. Stochastic differential equation of a Brownian Motion, Girsanov Theorem application to Geometric Brownian Motion, Theoretical distribution of (geometric) Brownian motion (with drift), Show that $(W_t, \int_0^t W_s ds)$ has a normal joint distribution, More questions about integral of Brownian Motion w.r.t time, Prove that $d\hat{W}_t = dW_t - \frac{1}{N_t} \cdot dN_t\cdot dW_t$ gives a Brownian motion under forward measure. Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. What's is the purpose of a trailing '-' in a Kubernetes apply -f -. Question 1 . Why is R_t (or R_0) and not doubling time the go-to metric for measuring Covid expansion? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Browse other questions tagged fa.functional-analysis pr.probability stochastic-processes stochastic-calculus brownian-motion or ask your own question. Why do I need to turn my crankshaft after installing a timing belt? CIE IGCSE Chemistry exam revision with questions and model answers for Diffusion, Brownian Motion, Solids, Liquids, Gases 1. Furthermore, what then is the meaning of $\int_0^T W_t \ln(W_t) dW_t$? 60 seconds . (a) The expected stock price at the end of the next day. Thanks for contributing an answer to Quantitative Finance Stack Exchange! @Magicisinthechain: out of curiosity, how would one interpret the integral $\int_0^T{W_T f(W_T) dW_t}$ (or $\int_0^T{W_t f(W_t) dW_t}$) ? Making statements based on opinion; back them up with references or personal experience. Quick link too easy to remove after installation, is this a problem? as the outcome of a betting game, where initially the bettor bets $W_0:=0$, but each subsequent moment in time, the bettor bets the realized sum (up to that point in time) of Brownian increments $W_{h+1}-W_h$. Making statements based on opinion; back them up with references or personal experience. Can you have a Clarketech artifact that you can replicate but cannot comprehend? Terms Where would it arise and what would it represent? Can this WWII era rheostat be modified to dim an LED bulb? For what modules is the endomorphism ring a division ring? But avoid … Asking for help, clarification, or responding to other answers. (25 Points) Suppose That A Stock Price Follows The Geometric Brownian Motion: DSt = U St Dt To StdW+ Where The Expected Rate Of Return U Is 16% And The Volatility O Is 30%. b) Osmosis ... c) Brownian Motion. Using of the rocket propellant for engine cooling. Q. What modern innovations have been/are being made for the piano, OOP implementation of Rock Paper Scissors game logic in Java. 3. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. (25 points) Suppose that a stock price follows the Geometric Brownian motion: dSt = u St dt to StdW+ where the expected rate of return u is 16% and the volatility o is 30%. SURVEY . Making statements based on opinion; back them up with references or personal experience.