Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

How to Get a Quant Job in Finance

financejobs.co

Post reply on HN
Print view View original

131–140 of 143 posts

Re: How to Get a Quant Job in Finance

#131

Post by foldr »

megrimlock wrote: post #130
murbard2 wrote: post #86

Earlier quoted context omitted.

Do you have experience interviewing candidates? Many candidates will answer this question correctly and yet be totally unable to do anything when they're confronted with a non textbook case. To be clear the brain teasers I ask are mathematical problems, not the type of brain teasers used in consulting interviews. For instance: We play a game where we each draw a secret random number uniformly between 0 and 1. We each…

Ok, I'm stumped. If I've parsed your description correctly, we get no info about our opponent's actions or the results until the end. Absent any ability to observe their strategy, it seems like you do want to maximize for expected value of your own actions, and I'm curious about the counterexample. How do we maximize EV? A single throw's pdf is 1, for x in [0,1], so its EV is 0.5. The question is how to improve on a…

I don't really get it either, but I think the idea is that you're supposed to somehow optimize on the assumption that your opponent is equally likely to be using any strategy. (To my mind this makes the problem very confusing because it's such an unrealistic assumption.) If you assume that the only possible strategies are "rethrow if my first throw is <= x", then you can define a function f(x,y) giving the EV where x is the threshold for your rethrow and y is the threshold for your opponent's. I guess you then integrate with respect to y (to get the EV for any given x assuming a uniform distribution for the opponent's choice of y) and then differentiate the result with respect to x to find the maximum? If the solution is along those lines that would explain the problem's supposed accessibility to good high school students.

Re: How to Get a Quant Job in Finance

#132

Post by murbard2 »

blahblah3 wrote: post #128
murbard2 wrote: post #86

Earlier quoted context omitted.

Do you have experience interviewing candidates? Many candidates will answer this question correctly and yet be totally unable to do anything when they're confronted with a non textbook case. To be clear the brain teasers I ask are mathematical problems, not the type of brain teasers used in consulting interviews. For instance: We play a game where we each draw a secret random number uniformly between 0 and 1. We each…

hey murbard is the answer to this 1-goldenratio? (.618...) to get this I computed the function f(x,y) which is my expected value if I reroll if roll <= x and my opponent re-rerolls if roll <= y. let p be the optimal value. by symmetry f(p,p) = 0.5 so there must be a local minimum around that point. solving by taking a one sided derivative gives me (sqrt(5)-1)/2

Indeed it is, isn't it a nice result? :)

(to be thorough, you also need to show that re-rolling based on a single threshold dominates other strategies, but it's fairly intuitive and not too hard to prove)

Re: How to Get a Quant Job in Finance

#133

Post by murbard2 »

upquark wrote: post #97
murbard2 wrote: post #86

Earlier quoted context omitted.

Do you have experience interviewing candidates? Many candidates will answer this question correctly and yet be totally unable to do anything when they're confronted with a non textbook case. To be clear the brain teasers I ask are mathematical problems, not the type of brain teasers used in consulting interviews. For instance: We play a game where we each draw a secret random number uniformly between 0 and 1. We each…

I wouldn't describe this as a brainteaser. It's a well-defined math problem, not some BS question about manhole covers or barbers in Chicago.

I suppose it depends on the industry then... These are what we tend to call brainteasers in quant finance, and they're the type of problems you'll find in the book "Heard on the street" recommended above.

Re: How to Get a Quant Job in Finance

#134

Post by murbard2 »

foldr wrote: post #131
megrimlock wrote: post #130

Earlier quoted context omitted.

Ok, I'm stumped. If I've parsed your description correctly, we get no info about our opponent's actions or the results until the end. Absent any ability to observe their strategy, it seems like you do want to maximize for expected value of your own actions, and I'm curious about the counterexample. How do we maximize EV? A single throw's pdf is 1, for x in [0,1], so its EV is 0.5. The question is how to improve on a…

I don't really get it either, but I think the idea is that you're supposed to somehow optimize on the assumption that your opponent is equally likely to be using any strategy. (To my mind this makes the problem very confusing because it's such an unrealistic assumption.) If you assume that the only possible strategies are "rethrow if my first throw is <= x", then you can define a function f(x,y) giving the EV where x…

The reason maximizing EV isn't the answer is that you care about having a larger number than your opponent, not about having the largest number possible.

Imagine we play a die game where whoever rolls the largest number wins. Which die would you rather play with?

1-1-1-1-1-10^250 or 2-2-2-2-2-2

The first die has an EV of about 1.67e249, the second die an EV of 2. Yet, the second die will win 5 out of 6 games against the other one.

To solve the problem, you must find the Nash equilibrium of the game. That is, you must find a strategy which the opponent cannot exploit, no matter what he does.

Re: How to Get a Quant Job in Finance

#135

Post by murbard2 »

foldr wrote: post #131
megrimlock wrote: post #130

Earlier quoted context omitted.

Ok, I'm stumped. If I've parsed your description correctly, we get no info about our opponent's actions or the results until the end. Absent any ability to observe their strategy, it seems like you do want to maximize for expected value of your own actions, and I'm curious about the counterexample. How do we maximize EV? A single throw's pdf is 1, for x in [0,1], so its EV is 0.5. The question is how to improve on a…

I don't really get it either, but I think the idea is that you're supposed to somehow optimize on the assumption that your opponent is equally likely to be using any strategy. (To my mind this makes the problem very confusing because it's such an unrealistic assumption.) If you assume that the only possible strategies are "rethrow if my first throw is <= x", then you can define a function f(x,y) giving the EV where x…

And no, you don't assume that every strategy is equally likely. You assume that the opponent plays optimally with full knowledge of your own strategy, which means you're looking for a Nash equilibrium http://en.wikipedia.org/wiki/Nash_equilibrium

Re: How to Get a Quant Job in Finance

#136

Post by murbard2 »

thecage411 wrote: post #106
murbard2 wrote: post #86

Earlier quoted context omitted.

Do you have experience interviewing candidates? Many candidates will answer this question correctly and yet be totally unable to do anything when they're confronted with a non textbook case. To be clear the brain teasers I ask are mathematical problems, not the type of brain teasers used in consulting interviews. For instance: We play a game where we each draw a secret random number uniformly between 0 and 1. We each…

I haven't read up on game theory in a long time, does "best strategy to follow" mean "the strategy that maximizes my expected payoff for all the strategies my opponent could employ"? So, an explicit counterexample would be my opponent picking a strategy of only re-throwing above .25. His expectation is then .25 * (0 + .25)/2 + .75 * (0 + 1)/2 ~= .40, so I should not rethrow if I get above .40 and below .50, even thou…

Don't focus on expectation, focus on probability of winning.

Re: How to Get a Quant Job in Finance

#137

Post by foldr »

murbard2 wrote: post #135
foldr wrote: post #131

Earlier quoted context omitted.

I don't really get it either, but I think the idea is that you're supposed to somehow optimize on the assumption that your opponent is equally likely to be using any strategy. (To my mind this makes the problem very confusing because it's such an unrealistic assumption.) If you assume that the only possible strategies are "rethrow if my first throw is <= x", then you can define a function f(x,y) giving the EV where x…

And no, you don't assume that every strategy is equally likely. You assume that the opponent plays optimally with full knowledge of your own strategy, which means you're looking for a Nash equilibrium http://en.wikipedia.org/wiki/Nash_equilibrium

That's fine if you already know game theory, but then the problem is not quite as accessible as you made out. You can't expect someone to just invent the concept of a Nash Equilibrium on the spot from the words "best strategy". (Although I understand that you may expect your interviewees to already be familiar with game theory.)

Re: How to Get a Quant Job in Finance

#138

Post by murbard2 »

foldr wrote: post #137
murbard2 wrote: post #135

Earlier quoted context omitted.

And no, you don't assume that every strategy is equally likely. You assume that the opponent plays optimally with full knowledge of your own strategy, which means you're looking for a Nash equilibrium http://en.wikipedia.org/wiki/Nash_equilibrium

That's fine if you already know game theory, but then the problem is not quite as accessible as you made out. You can't expect someone to just invent the concept of a Nash Equilibrium on the spot from the words "best strategy". (Although I understand that you may expect your interviewees to already be familiar with game theory.)

In this case, the candidate's thesis work explicitly dealt with game theory. In addition, this doesn't require much knowledge of game theory... if you think about the problem for a bit, you can re-derive the concept fairly easily.

Nash's brilliance was in proving that under reasonable conditions, a mixed equilibrium always exists, which is far less obvious.

Re: How to Get a Quant Job in Finance

#139

Post by foldr »

murbard2 wrote: post #138
foldr wrote: post #137

Earlier quoted context omitted.

That's fine if you already know game theory, but then the problem is not quite as accessible as you made out. You can't expect someone to just invent the concept of a Nash Equilibrium on the spot from the words "best strategy". (Although I understand that you may expect your interviewees to already be familiar with game theory.)

In this case, the candidate's thesis work explicitly dealt with game theory. In addition, this doesn't require much knowledge of game theory... if you think about the problem for a bit, you can re-derive the concept fairly easily. Nash's brilliance was in proving that under reasonable conditions, a mixed equilibrium always exists, which is far less obvious.

The issue isn't the difficulty of the concept but the ambiguity of "best strategy".

Re: How to Get a Quant Job in Finance

#140

Post by murbard2 »

foldr wrote: post #139
murbard2 wrote: post #138

Earlier quoted context omitted.

In this case, the candidate's thesis work explicitly dealt with game theory. In addition, this doesn't require much knowledge of game theory... if you think about the problem for a bit, you can re-derive the concept fairly easily. Nash's brilliance was in proving that under reasonable conditions, a mixed equilibrium always exists, which is far less obvious.

The issue isn't the difficulty of the concept but the ambiguity of "best strategy".

Fine, best strategy given a perfectly rational opponent. There, ambiguity removed.
Post reply on HN