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Nonlinear5, the recursive solution avoids the combinatorial explosion. The way it is implemented is via a Bellman equation (more here: http://en.wikipedia.org/wiki/Bellman_equation). Essentially, the goal is to solve for the optimal allocation on the final spin as a function of W and B_9...

Dividends can result in different IVs for calls and puts (dividends can change the effective moneyness and expiration). Also, if a stock is hard to borrow, put-call parity doesn't necessarily hold.

They are equivalent. W(0) is just a constant. Max E[log(W(N)/W(0))] is the same problem as max E[log(W(N))]. You can pull W(0) out of the logarithm as follows: E[log(W(N)/W(0))] = E[log(W(N)] - log(W(0)) Note that argmax f(x) + constant is the same as argmax f(x).

I have seen this type of game offered as a promotion from betting sites like Bodog. For example, "Open a new account and bet up to $1000 on the Super Bowl money line. If you lose, we'll cover your loss." Also, if you think about this more abstractly, calling "bank roll" to be "what you have...

Well, I'm not suggesting to bet your entire worth, just to take it into account deciding the optimal wager. There is no "correct" answer here because the OP does not specify an objective function. If you take the objective to be "maximize the expected log of the initial $1000 bankroll after 10...

That's correct. If W is large (say $1mn), I believe betting $1,000 on R16 maximizes the expected log of liferoll in your one-spin example. Goal: Max E[log(W + B_1)] Candidate solution: Bet $1000 on R16. B_1 = $36,000 with probability 4/37 B_1 = $0 with probability 33/37 E[log(W + B_1) =...

Agreed that 100% would be wagered, but the allocation across bets would vary. The arbitrage has a lower expected return than the riskier R-16. Presumably, the allocation to R-16 would increase as you get closer to the final spin.

Treat B_9 as a variable and solve for the optimal xj_10 as a function of B_9. It gets cumbersome quickly. That's why I was suggesting maximizing the risk neutral expectation, not expected logarithm. Not only are there some assumptions where this is optimal (i.e., ability to diversify by selling...

For a utility function, you could still use expected log of terminal wealth. This is a constrained maximization problem, where the key constraint is the initial bet cannot exceed $1000, and no bet can exceed what the $1000 bankroll has grown to. You could work backwards to solve the problem...

Suppose you are worth $1,000,000. Suppose you can bet up to $1,000 on just one spin, with the same odds given in the OP. How much would you bet? If your goal is to maximize geometric mean returns, it should be for the $1,000,000 net worth, not the $1,000 you are allowed to wager. When people are...

Thanks for the link. I am familiar with the Kelly criterion (have an economics phd, studied dynamic programming problems like this ad nauseam in my first year macro sequence). The reason I think we differ is due to what you are considering the maximization problem. You are assuming we would...

Only had time to browse a few pages, but what struck me was that everyone seemed to assume the optimal strategy does not change with spin number. If we assume the goal is to maximize the expected value of terminal wealth after 10 spins, the optimal bet changes with each spin. In particular, on...

I'd be curious to hear about the events that led you to the wisdom in your post.

Trading is so hard, I could explain my edge to 99% of people, and they still wouldn't make money on it, let alone find the edge to begin with.

FAZ = -1 x FAS intraday SKF = -2/3 x FAS intraday If you want the same volatility, just buy more shares. I don't understand the need to short FAS for a day trade.

Tomorrow, I think we'll finally get a selloff. I rarely buy puts, but with the VIX at 24.30 and the market short-term overbought, I couldn't help myself this afternoon.

Fifth grade sex ed class, I raise my hand and ask, "How do you know when you're done?" (Having sex, that is.) After lots of laughter (I was young for my grade), the teacher replies, "Oh, you'll know." Same goes for having an edge.

You must be swinging a massive line if SPX vol makes a difference to your trading.

Short ES Long ZB Looking forward to tomorrow.

Yes, one leg of the trade is to short the JGB futures, which is effectively a fixed-to-floating swap with the borrowing done in yen. The second leg of the trade is to buy a higher yielding asset.