Chapter 6 of Cover & Thomas’ “Elements of Information Theory” gives good info on the Kelly criterion, how to derive it, and the relations between prices/probabilities and entropy/rate of return.

For math finance, the class I took back in college used Shreve’s “Stochastic Calculus for Finance II”. I wouldn’t necessarily recommend that just to learn about this, but it’s a good source for brownian motion, some basic measure theory, and the core theory of asset pricing.

Typically complete markets come up in discussing the fundamental theorem of asset pricing. The first part of the theorem says that any arbitrage-free set of asset prices has a “risk-neutral measure”, i.e. a market-implied set of probabilities. The second part says those probabilities are unique iff the market is complete—if some bets can’t be placed, then there are multiple possible market-implied probabilities. Any book which covers the fundamental theorem should have at least some coverage of complete markets.

Finally, if you’re looking for something more applied, Hull’s “Options, Futures and Other Derivatives” is the usual starting point.

Can you recommend me a good textbook that covers these things? I know basic econ (Krugman and Wells) and a bunch of probability and game theory.

Chapter 6 of Cover & Thomas’ “Elements of Information Theory” gives good info on the Kelly criterion, how to derive it, and the relations between prices/probabilities and entropy/rate of return.

For math finance, the class I took back in college used Shreve’s “Stochastic Calculus for Finance II”. I wouldn’t necessarily recommend that just to learn about this, but it’s a good source for brownian motion, some basic measure theory, and the core theory of asset pricing.

Typically complete markets come up in discussing the fundamental theorem of asset pricing. The first part of the theorem says that any arbitrage-free set of asset prices has a “risk-neutral measure”, i.e. a market-implied set of probabilities. The second part says those probabilities are unique iff the market is complete—if some bets can’t be placed, then there are multiple possible market-implied probabilities. Any book which covers the fundamental theorem should have at least some coverage of complete markets.

Finally, if you’re looking for something more applied, Hull’s “Options, Futures and Other Derivatives” is the usual starting point.

Thank you!