These lecture notes summarize standard machinery of an advanced course on Mathematics of Arbitrage. This note is based … understood as a complementary material to the book of F. Delbaen and W. Schachermayer "Mathematics of Arbitrage" published with …

start from two simple, economically motivated axioms, namely absence of arbitrage (in the sense of NUPBR) and absence of … relative arbitrage among all buy-and-hold strategies (called static efficiency). A valuation process for a payoff is then … valuing by absence of arbitrage alone. We show that this always yields put-call parity, although put and call values …

We prove the existence of statistical arbitrage opportunities for jump-diffusion models of stock prices when the jump …-size distribution is assumed to have finite moments. We show that to obtain statistical arbitrage, the risky asset holding must go to … zero in time. Existence of statistical arbitrage is demonstrated via 'buy-and-hold until barrier' strategy, where the …