General theory of pricing and hedging in incomplete markets, its symbolic implementation, and applications

Abstract: We present an overview (and some details, time-permitting) of the author's general theory of optimal and indifference portfolio pricing and hedging for diffusive Markovian incomplete markets. The general theory is implemented symbolically on Mathematica computer platform. As such, the symbolically implemented general theory is the single most powerful math-finance methodology for solving pricing (and hedging) problems today. For example, as it will be shown, well-known published papers on indifference pricing (and hedging) can be derived and very much generalized (after model coefficients are typed-in) in a fraction of a second. We shall discuss also some applications of the general theory such as: 1) derivation of an explicit incomplete-market bond pricing formula capable of explaining a transition from a normal yield curve into a humped yield curve, 2) the bid/ask price spread and its dependence on various market parameters, etc. The main reference: S. Stojanovic, Neutral and Indifference Portfolio Pricing, Hedging and Investing, Springer, New York, 2012 (https://www.amazon.com/dp/0387714170).

HOST: Gunduz Caginalp