<t>Function have a rotation symmetry around 0. So, when you integrate the function over a domaine x>0, x<z (x-y=z, y<0) you get 1/8 of the integral over the whole plane.Another way to see the result is to see that events W(1)>0, W(2)-W(1)<0 and abs(W(1))<abs(W(2)-W(1)) are independent, with probabil...

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QuoteOriginally posted by: mhughesLet A be the fraction of times for which a_m = 1, i.e. and define B and C similarly. .These limits are not necessarily exist.Imagine the sequence 0 11 0000 11111111 ....

QuoteOriginally posted by: LapinRe reading the problem, I am not sure I fully understood the question.My solution should work if they ask everyday, but it should not be true after few days.They are asked only at the end, when they already dispose an infinite sequence of 0s and 1s.

<t>Three wise men are locked in three rooms. Each day there there is, or there is no light in each room.During a certain finite initial period there is no rule about how the rooms are illuminated, and after one of two cases are possible:1. Each day exactly one room is illuminated2. Each day exactly ...

I guess the magician should not see the board with initial coins distribution. In this case the question makes more sense for me

<t>Move all the rooks o the bottom layer along the vertical (Using sevvost pictures it means that there will be a rook in each square where there is a number). Probably there will be more than 1 rook in certain squares.Let's denote the number of rooks in rows and number of rooks in columns. We can a...

<t>For a cube kxkxk it's easy to put rooks in a way that each row (in all 3 direction) contains 1 rook). Exemple : coordinates i,j,(i-j) mod k for every i,jThan for the cube (k1+k2)x(k1+k2)x(k1+k2) we can put rooks satisfying initial requirements. (Placing in smaller cubes of sizes k1xk1xk1 and k2xk...

<t>Thanks for your answer.I do not see easy relationships between the expected variance and implied volatility. If I price an option using ARCH model for volatility do I have smile and leverage effect? Even if I use some kind of SV model (GARCH?) and calibrate it to observable option prices (short-d...

<t>You can apply for a job without work visa, many of my friends did so. The only problem is that you will not be able to start work immediately and this can be a problem for certain companies. But in general, if a company is really interested in your candidacy, they accept to wait. HSMP is probably...

<t>Are there any suggestions about extrapolation of the single stock implied volatility for a long maturity?The available information is the implied volatility for the shorter maturities, and possibly the long-dated vol for the index containing this stock.Surprisingly, I havn't found any papers or t...