These integrals have a very clear math definition and sometimes appear in option pricing. Or asked another way, is there an $ARIMA(p,d,q)$ model that "corresponds to" geometric Brownian motion? Making statements based on opinion; back them up with references or personal experience. CIE IGCSE Chemistry exam revision with questions and model answers for Diffusion, Brownian Motion, Solids, Liquids, Gases 1. Question 1 . I am sure there will be more thorough answers provided by others, but let me have a quick go at the first part: "what is meant by $\int_0^T W_t dW_t$ in finance?". (c) The 95% confidence limits for the stock price at the end of the next day. How many lithium-ion batteries does a M1 MacBook Air (2020) have? Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. 20 Questions Show answers. Is it too late for me to get into competitive chess? In a similar vein, would showing that an $ARIMA(0,1,0)$ model fits the logged energy prices vindicate the assumption of a geometric Brownian motion? b) Osmosis ... c) Brownian Motion. If $W_t$ is standard Brownian motion, what is $\int_0^T W_t \ln(W_t) dW_t$? $X_h\epsilon${$-1,1$} with probability $0.5$), $Y_h=1$ and $f()=2$. What would result from not adding fat to pastry dough. For what modules is the endomorphism ring a division ring? Do aircraft that operate at lower altitudes tend to have more cycles? CIE IGCSE Chemistry exam revision with questions and model answers for Diffusion, Brownian Motion, Solids, Liquids, Gases Multiple Choice 2. This quantity computes the outcome of a gambling game after 10 rounds of betting, where each round the bettor bets consistently 1 unit of currency, and can either win or lose twice what he or she bets. answer choices . Furthermore, what then is the meaning of $\int_0^T W_t \ln(W_t) dW_t$? Using of the rocket propellant for engine cooling. This looks right to me, but maybe someone will have more to say! Then a discrete Stochastic integral (finite sum, strictly speaking not an Ito integral) could be defined as: $I_{t=10}=\sum_{h=0}^{9}2\left(X_{h+1}-X_h\right)$. Use MathJax to format equations. Question: 3. Please be sure to answer the question. Thanks for contributing an answer to Quantitative Finance Stack Exchange! In general, Ito Integral can be written as: $$I_t:=\int_{h=0}^{h=t}f(Y_h)dX_h=\lim_{n \to\infty}\sum_{h=0}^{n-1}f(Y_h)\left(X_{h+1}-X_h\right)$$. rev 2020.11.24.38066, The best answers are voted up and rise to the top, Quantitative Finance Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Also, what do you mean with ''what do these integrals mean in finance?'' Quick link too easy to remove after installation, is this a problem? For a student studying Chinese as a second language, is there any practical difference between the radicals 匚 and 匸? I have read that Brownian motion, or more precisely, a Wiener process, is a scaling limit of a random walk. In sequence models, is it possible to have training batches with different timesteps each to reduce the required padding per input sequence? What if the P-Value is less than 0.05, but the test statistic is also less than the critical value? 60 seconds . b) Osmosis ... c) Brownian Motion. perhaps you can tell the other poster to correct $T$ to $t$ as well, Hi @develarist: It's a good question, I think intuition is always important in finance. d) Absolute zero Tags: Question 3 . Illustrative example: let's suppose $X_h$ represents a coinflip for each $h$ (i.e. answer choices . Where would it arise and what would it represent? Are you sure you mean $\int_0^T W_TdW_t$ and not $\int_0^T W_tdW_t$? Featured on Meta “Question closed” notifications experiment results and graduation Is Elastigirl's body shape her natural shape, or did she choose it? I had a crack at the intuition behind Ito Integrals of the type $\int_0^TW_t\,dW_t$ in this answer. Moving on, taking $X_t=W_t$, $Y_t=W_t$ and $f()=1$, I interpret the Ito integral $$I_t:=\int_{h=0}^{h=t}W_hdW_h=\lim_{n \to\infty}\sum_{h=0}^{n-1}W_h\left(W_{h+1}-W_h\right)$$.