tag:blogger.com,1999:blog-93032862025-05-11T16:41:26.080-07:00optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.comBlogger90125tag:blogger.com,1999:blog-9303286.post-71306993343756318572020-03-05T11:26:00.000-08:002020-03-05T12:41:01.989-08:00

\( \eta(s) = (1-2^{1-s}) \zeta(s) \) general form, for \( p \in \mathbb{N} \) \( \zeta(s) = \dfrac{1}{1^s} + \dfrac{1}{2^s} + \dfrac{1}{3^s} + ... \) \( \dfrac{p}{p^s} \zeta(s) = \dfrac{p}{p^s} + \dfrac{p}{{(2p)}^s} + \dfrac{p}{{(3p)}^s} + ... \) for \( p=3 \) \( \zeta(s) - \dfrac{p}{p^s} \zeta(s) = \dfrac{1}{1^s} + \dfrac{1}{2^s} - \dfrac{2}{3^s} + \dfrac{1}{4^s} + \dfrac{1}{5^s} - \dfrac{2

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-46436090832882266112019-04-25T19:40:00.002-07:002025-05-11T16:12:28.339-07:00

update: 2025.03.20 基本所得額在750萬元以下者，可扣除750萬元，沒有繳納基本稅額之問題；基本所得額超過750萬元者，先扣除750萬元後，再就其餘額按20％稅率計算基本稅額。基本稅額＝(基本所得額－750萬) × 20%

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-51599299221479134172019-03-13T17:34:00.001-07:002019-03-13T17:34:42.430-07:00

道理基本上 很簡單 就是 多賺錢 多存錢 不要亂花錢 你自然就會變有錢 一般來說 所謂的有錢 一種是看淨資產  另一種是看可用來做投資的淨資產 (自住的房子的價值要先扣掉) 一般小額花費的標準是  萬分之一的消費額度(每日)  不太需要考慮...  萬分之 365  約等於 3.65%...  所以以正常的投資報酬率 就能夠支付 所以有一百萬美金的可投資資產  就大約是一百元美金 約台幣三千元  以這種花錢速度  應該一輩子也花不完 另外 以投資的角度  如果能及早投資在適當的標的  以美國標普500 長期投報率約 6.6%(扣掉通膨) 而言  你從25歲工作40年  65歲退休  預期壽命為85歲 那你從工作開始  每月存台幣一

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-71703121894156932222019-02-27T01:58:00.002-08:002019-02-27T01:58:28.353-08:00

Data: $SPY from 1-19-2007 Adjusted by daily closing prices Starting capital is $10,000. Neglecting dividends and the borrowing cost. The blue line is the baseline.

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-23863403107361178592019-01-22T03:37:00.001-08:002019-01-22T18:45:36.966-08:00

If we want to create a leveraged portfolio tracking an index, we need to know how to maintain a constant leverage ratio.  The concept is pretty simple. Say if we want to maintain a leverage ratio, $L = 2$.  If the index $I$ moves $\delta$ percent.  Our portfolio $\pi$ will move $2\delta$ percent. Assuming the borrowing cost is zero. Our initial capital is $C$. So at the

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-23879369357957037832017-11-30T20:20:00.001-08:002017-11-30T20:20:59.046-08:00

$\vec{a}:\text{the unknown vector of the system parameters}$ $\vec{x}:\text{the vector of the input signal }$ $y:\text{the output signal }$ $y=\vec{a}\cdot\vec{x}$ $\vec{a}^{\prime}:\text{the vector of the prior estimated parameters}$ $\text{the estimated output}: y^{\prime}=\vec{a}^{\prime}\cdot\vec{x}$ $\text{error}:e=y-y^{\prime}$ $\vec{a}^*:\text{the vector of the posterior estimated

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-59998415512586653262017-06-22T17:01:00.001-07:002017-06-22T17:01:09.112-07:00

$Result = {Technology} ^ {Business Skills}$ Technology Business Skills Result 0 * 0 1 0 1 1 1 1 1 2 1 2 0 1 2 1 2 2 2 4 2 3 8

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-29399076814140269242017-04-28T20:52:00.001-07:002017-04-28T20:52:17.509-07:00

From the point of view of the measurement, we can make a prediction of the measurement ${\textbf{z}_1}'$ from ${\textbf{x}_1}'$, and we can get $({\textbf{z}_1}', \textbf{H}_1{\textbf{P}_1}'\textbf{H}_1^T)$. The measurement is $(\textbf{z}_1, \textbf{R}_1)$, the estimate is $\textbf{z}_1^* = (\textbf{I}-\textbf{G}_1){\textbf{z}_1}'+\textbf{G}_1\textbf{z}_1$ a good estimate comes with $\textbf

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-23790646010872233552017-04-28T07:39:00.001-07:002017-04-28T07:39:05.990-07:00

Here is the chart of the probability distribution of a 1D example on the (prediction, measurement, estimate) for the normal distribution case. As we can see, both the measurement and the prediction are unbiased, but have different probability distributions.  By adjusting the weight, we can find a better unbiased estimation.

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-19686483787602801992017-04-27T07:25:00.001-07:002017-04-27T07:25:07.209-07:00

Some ideas about the Kalman filter. Say we have a dynamic system that has the internal state $\textbf{x}$ and the control input $\textbf{u}$.  Although we don't know the internal state $\textbf{x}$, we can observe it and have the measurement $\textbf{z}$. Then how can we estimate the internal state $\textbf{x}$? At first, we may have an initial estimated state and the covariance $(\textbf

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-20155692137119850812017-04-26T02:02:00.001-07:002017-04-26T02:02:19.798-07:00

From the previous example, we know if we want to merge two data, we also need the standard deviation or variance of the data in order to make a better estimation.  By following the tradition, we will use variance for the following derivations. Say the data fusion process is defined as: $d_f = \mathcal{F}(d_1,d_2)$, $d_i = (x_i,\sigma_i^2)$ To have a good estimate means to have an unbiased

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-8022554733153685122017-04-25T09:32:00.001-07:002017-04-25T21:42:27.898-07:00

Let's say we want to measure the resistance of a resistor with an ohmmeter.  The measured value is $z$ with a standard deviation $\sigma$.  Assuming the resistance is $x$. The measurement is like $z=x+v$ and $v$ is the measurement noise with mean $0$ and standard deviation $\sigma$. If we only take one measurement, we get an estimation $z_1$ for the $x$.  The standard deviation

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-14766833101032836272017-04-06T19:18:00.000-07:002017-04-06T19:18:58.880-07:00

聽力    在初期  建議可以上美國的購物網站  找有直播的練習聽力  例如 QVC 因為這些英語都算標準  而且一直重複一個話題    進步到一定的程度以後  就可以試試新聞 CNN 財經網站 Bloomberg 或其他 教育性的節目 Discovery    當然最後如果能看得懂 電視節目  電影  那就算相當不錯了 閱讀能力    可以找本介紹速讀的書  看看如何增加閱讀的速度    基本的原理  就是 眼球的控制  一開始可以拿一把尺練習  用尺幫助一行一行的閱讀  遮住下方的英文字    閱讀時  眼球由左到右 &

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-58887349909998595392016-07-20T21:19:00.000-07:002016-07-21T02:09:03.226-07:00

basic concept: Nutrition and Calorie Controlled Diet with Fitness Exercises. ------------------------------------------------------------ To lose your weight is just a calorie counting game.  If you take in 2000 Cals and spend 2100 Cals a day, you lose your weight.  100 Cals a day may help you lose 11~25 grams a day.  It seems not much, but think about it, 10 grams a day is 3.65

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-113665676539879202016-04-23T23:48:00.002-07:002016-04-23T23:49:28.331-07:00

Sometimes people want to make money on the trade, but not bring the seller and the buyer together, because the discrepancy of the price between those two parties.  Those people who make money on the price inefficiencies are arbitrageurs.  They can make almost risk-free profits if they handle those trades correctly. So what arbitrageurs want is not a well-developed market.  In a

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-592028948190407302016-04-23T20:43:00.001-07:002016-04-23T20:43:47.851-07:00

Another way to bring the sellers and the buyers together is by building a platform, such that the sellers can list their products there and also disclose the preferred selling/retail price on the products.  At the same time the buyers can see what the sellers offer, or even bid up the price of the product if the supply is limited. Usually the platform will charge a certain amount of money

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-73350410903430070322016-04-23T18:47:00.000-07:002016-04-23T18:47:10.370-07:00

A business or a trade has at least two roles, the seller and the buyer.  Of course, usually the seller who has the goods wants to trade it for money.  The buyer would pay the money and want to get the goods in return. Sometimes the seller doesn't have a good network to know who want to buy his product, or does not know if there is any potential to get a better price with his product.

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-75686740152655520502016-04-23T18:23:00.000-07:002016-04-23T18:23:03.330-07:00

I was trained as an engineer, so basically my mindset is more like learning new technologies to get employed and well-paid by a good company.  I am good at problem solving and also reading technical references and datasheets.  But I didn't have much sense on making money until I started my career at a software company. After I got some stock options from the company, I started

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-61933283405424544762015-03-02T09:24:00.000-08:002015-03-02T09:25:03.118-08:00

So how large is q, q is the winning rate when there is no 7, but any TJ combinations for the 5 cards on the table. Let's check the possible 5 card combinations: (assuming pocket pair is 7s7c, player X has TdJd) Case 1. You make a flush, the combination of the 5 card is    a. five spade (including Ts or Js or both): C(11,4)+C(11,4)-C(10,3)=540        less five

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-26433259276182486852015-03-02T05:47:00.000-08:002015-03-02T05:49:14.381-08:00

With continuing our previous discussion, say if you have pocket pair 77(no diamond), the other player X has TJ (suited-diamond).  Let's check the probability of player X getting a diamond flush. The remaining 5 cards has: 1. 3 diamond cards: C(11,3)*C(37,2)=109,890     straight-flush: 4*C(37,2)=2,664     a) 789TJ to TJQKA: 4 2. 4 diamond cards: C(11,4)*C(37,1)=12,210 &

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-2618454706467390952015-03-01T23:13:00.001-08:002015-03-02T02:52:30.584-08:00

With continuing our previous discussion, say if you have pocket pair 77, the other player X has TJ (not suited). 1.Player X could get a 789TJ straight: In case b, with a 7, but no TJ:   b.1) 789yz: 2*4*4*C(28,2)  yz not in (7,8,9,T,J,Q) Sum of (b.1) is 12,096, the probability is about 0.71%.  In case c,   c.1) 789Ty, 789Jy: 2*4*4*3*C(28,1)*2=5,376, the

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-31142686701983085112015-03-01T21:40:00.000-08:002015-03-02T02:49:39.771-08:00

Say if you have pocket pair 77, the other player X has AJ (not suited).  What's your probability of winning before the flop? Possible remaining 5 card combinations: 1,712,304=48*47*46*45*44/5!=C(48,5) Let's try to calculate the upper bound of the probability by listing out the possible cases. The remaining 5 cards: a) Without 7, A, J: 658,008=C(40,5)  the number of remaining cards

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com1tag:blogger.com,1999:blog-9303286.post-66530070334123589812014-09-29T08:56:00.001-07:002014-09-29T08:56:29.771-07:00

From the previous discussion, we assumed that the players play any kind of starting hands.  Or we should say that the probability distribution is the same for each starting hand. If a player is selective on the starting hands with considering each player's chips, strategy, style, and position,  the probability of each starting hand will be different. So the estimated probability of

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-91309398809484782252014-09-22T20:27:00.001-07:002014-09-22T20:27:42.655-07:00

With your two hole cards, the other players might have... Possible starting hands: 1081=47*46/2=C(47,2) Assuming the flop is 99K, a) if you flop a three of a kind with 9x Four of Kind: 0 Three of a Kind or Full House: 1*46+3=49  type 1: 9y, type 2: KK Two Pair: 3*43+10*6+3=192  type 1: Ky, type 2: yy, type 3: xx Others: 43*42/2-(10*6+3)=840  any combination without 9 and K

optTraderhttp://www.blogger.com/profile/05761729947199448308noreply@blogger.com0tag:blogger.com,1999:blog-9303286.post-14655622673543465672014-09-22T19:19:00.006-07:002014-09-22T19:38:56.225-07:00

As we might see a paired flop about 17% of time, let's take a look at what kind of hands players might have. Possible starting hands: 1176=49*48/2=C(49,2)  we can see here the possible starting hands are updated based on the flop (based on the fact). Four of a Kind: 1 Three of a Kind or Full House: 2*47 + 3 = 97  type 1: pick one card with the same number as the paired card(2) and

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